{"unique_id": "1obj_2rel_2extra_gen0001", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is an obtuse triangle ABC. There is a line segment AD. There is a line segment BE. There is a line segment FG. Line AD is an altitude of triangle ABC from vertex A. Line BE is a median of triangle ABC from vertex B. Lines AD and BE intersect at point H. Line FG is the perpendicular bisector of line BE, intersecting it at point E. Further, length of line AD is equal to length of line BE. Further, angle BAD is 30 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangleABC = scene.add.obtuse_triangle(A, B, C)\nline_altitude = scene.add.line_segment(A, D)\nline_median = scene.add.line_segment(B, E)\nline_perp_bisector = scene.add.line_segment(F, G)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude, triangleABC, A)\nscene.relate.is_median(line_median, triangleABC, B)\nscene.relate.lines_intersect_at(line_altitude, line_median, H)\nscene.relate.perpendicular_bisector_at(line_median, line_perp_bisector, E)\n\n### Extra relationships\n\nscene.constraint.eq(line_altitude.length, line_median.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 30)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "obtuse_triangle(A, B, C)", "line_altitude": "line_segment(A, D)", "line_median": "line_segment(B, E)", "line_perp_bisector": "line_segment(F, G)"}, "Rels": ["is_altitude(line_altitude, triangleABC, A)", "is_median(line_median, triangleABC, B)", "lines_intersect_at(line_altitude, line_median, H)", "perpendicular_bisector_at(line_median, line_perp_bisector, E)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_altitude').length, scene.get_object('line_median').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 30)"], "possible_solution": {"points": {"A": [-3.500043755695574, 0.94462274756542], "B": [1.5854318531471563, 1.5754688009160434], "C": [-0.41097961645851505, -3.1440878279943023], "D": [0.5872278499480432, -0.7843184553284344], "E": [-1.955513154308784, -1.099730194500732], "F": [-1.5794948298506821, -1.5974321090277124], "G": [-2.3315169464201966, -0.602040969296402], "H": [-0.7752020499681253, -0.20800227181936784]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0002", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a triangle with vertices A, B, and C. There is a line segment AD. There is a line segment BE. There is a line segment FG. Line AD is an altitude of triangle ABC from vertex A. The extensions of line AD and line BE intersect at point H. Further, length of line AD is equal to length of line BE and angle BAD is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\nline_altitude = scene.add.line_segment(A, D)\nline_median = scene.add.line_segment(B, E)\nline_perp_bisector = scene.add.line_segment(F, G)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude, triangleABC, A)\nscene.relate.line_extensions_intersect_at(line_altitude, line_median, H)\n\n### Extra relationships\n\nscene.constraint.eq(line_altitude.length, line_median.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "line_altitude": "line_segment(A, D)", "line_median": "line_segment(B, E)", "line_perp_bisector": "line_segment(F, G)"}, "Rels": ["is_altitude(line_altitude, triangleABC, A)", "line_extensions_intersect_at(line_altitude, line_median, H)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_altitude').length, scene.get_object('line_median').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 90)"], "possible_solution": {"points": {"A": [1.716816959296514, 8.630913714931514], "B": [-4.1272910287786875, -7.5742908699299], "C": [-0.9589882113761882, 0.8909190268987163], "D": [1.911674007874063, 8.56064213675728], "E": [-4.000590305692983, -7.410450953758003], "F": [-6.055448910625371, -9.988189369070737], "G": [-0.7786543412057987, 3.3272878804616597], "H": [6.948738317265704, 6.747294175520871]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0005", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a quadrilateral with vertices A, B, C, D. There is a line segment AC. There is a line segment BD. There is a line segment AB. Line AB is parallel to line AC. Line AC is perpendicular to line BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\nquadrilateral1 = scene.add.quadrilateral(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_AB = scene.add.line_segment(A, B)\n\n### relationships\n\nscene.relate.parallel(line_AB, line_AC)\nscene.relate.perpendicular(line_AC, line_BD)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"quadrilateral1": "quadrilateral(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_AB": "line_segment(A, B)"}, "Rels": ["parallel(line_AB, line_AC)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D"], "extra_rel": [], "possible_solution": {"points": {"A": [-3.0038797153799823, 1.6180145596299593], "B": [-3.4538348222856405, 1.8427389345620997], "C": [-0.4514881821392421, 0.34325496247383225], "D": [-4.292325391750234, 0.1638684766701279]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0007", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a circle with center A. There are line segments BC and DE. The extension of line BC intersects the circle at points B and C. Line BC is perpendicular to line DE. Further, the length of line BC is equal to the length of line DE and the angle BAC is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ncircle1 = scene.add.circle(A)\nline_seg1 = scene.add.line_segment(B, C)\nline_seg2 = scene.add.line_segment(D, E)\n\n### relationships\n\nscene.relate.line_extension_intersects_circle_at(line_seg1, circle1, B, C)\nscene.relate.perpendicular(line_seg1, line_seg2)\n\n### Extra relationships\n\nscene.constraint.eq(line_seg1.length, line_seg2.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_seg1": "line_segment(B, C)", "line_seg2": "line_segment(D, E)"}, "Rels": ["line_extension_intersects_circle_at(line_seg1, circle1, B, C)", "perpendicular(line_seg1, line_seg2)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_seg1').length, scene.get_object('line_seg2').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [-0.43144048890105596, -0.8062527401476122], "B": [-1.7938108257781344, 1.9846313045798016], "C": [-3.2223245340514812, -2.168623074276519], "D": [1.529496190417928, 1.031927025574673], "E": [-2.6237581805428762, 2.4604407400938952]}, "circles": {"A": 3.105653990743581}}}
{"unique_id": "1obj_2rel_2extra_gen0008", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a kite ABCD. There is a line AC. There is a line BD. There is a line BE. Line AC is perpendicular to line BD. Line BE is the angle bisector of angle ABD. Further, length of line AC is equal to length of line BD. Further, angle ABD is 45 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nkite1 = scene.add.kite(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_angle_bisector = scene.add.line_segment(B, E)\n\n### relationships\n\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.angle_bisector(A, B, D, line_angle_bisector)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('D')), 45)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"kite1": "kite(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_angle_bisector": "line_segment(B, E)"}, "Rels": ["perpendicular(line_AC, line_BD)", "angle_bisector(A, B, D, line_angle_bisector)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('D')), 45)"], "possible_solution": {"points": {"A": [0.1013207498231788, -2.768698081667471], "B": [-4.390236670300434, -4.148769509490379], "C": [-5.770308106247534, 0.3427879076567602], "D": [-1.2787506473380637, 1.7228594125873589], "E": [1.582096683067135, 0.7884720202970505]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0009", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a circle with center A. There is a line segment BD. There is a line segment AC. There is a line segment ED. Line BD is a diameter of the circle. Angle EAC is acute.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_ED = scene.add.line_segment(E, D)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.acute_angle(E, A, C)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_ED": "line_segment(E, D)"}, "Rels": ["is_diameter(line_BD, circle1)", "acute_angle(E, A, C)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [1.012827765497733, 2.30426237162474], "B": [0.6766183155419712, 2.067457741352174], "C": [-9.35794968337524, -10.0], "D": [1.349037218819736, 2.5410670048981947], "E": [1.4169908481320719, 0.41692359843616167]}, "circles": {"A": 0.4112337916427173}}}
{"unique_id": "1obj_2rel_2extra_gen0010", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a rectangle with points A, B, C, D. There are line segments AC and BD. Line AC is perpendicular to line BD. Further, length of line AC is equal to length of line BD and angle ABC is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\n\n### relationships\n\nscene.relate.perpendicular(line_AC, line_BD)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)"}, "Rels": ["perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [10.0, -10.0], "B": [10.0, 10.0], "C": [-10.0, 10.0], "D": [-10.0, -10.0]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0012", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a minor arc BC with center A. There is a line segment AD. There is a line segment BE. There is a line segment CE. Angle DAB is bisected by line AD. Point E lies on the minor arc BC. Further, length of line AD is equal to length of line BE and angle ABC is 60 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\narc1 = scene.add.minor_arc(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CE = scene.add.line_segment(C, E)\n\n### relationships\n\nscene.relate.angle_bisector(D, A, B, line_AD)\nscene.relate.point_lies_on(E, arc1)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BE.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 60)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"arc1": "minor_arc(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CE": "line_segment(C, E)"}, "Rels": ["angle_bisector(D, A, B, line_AD)", "point_lies_on(E, arc1)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 60)"], "possible_solution": {"points": {"A": [1.5949643521261672, -3.431032230997176], "B": [2.8580745641048155, 0.383199110555249], "C": [-1.0767017851207312, -0.43003102694400097], "D": [2.6499982032221094, -0.24513202362426748], "E": [-0.4773014041741488, 0.011281355603919524]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0013", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is an isosceles trapezoid ABCD. There is a line CD. Trapezoid ABCD is a mirror image of itself across line CD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ntrapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)\nline_m = scene.add.line(C, D)\n\n### relationships\n\nscene.relate.mirror_across_line(trapezoid1, trapezoid1, line_m)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "isosceles_trapezoid(A, B, C, D)", "line_m": "line(C, D)"}, "Rels": ["mirror_across_line(trapezoid1, trapezoid1, line_m)"], "Points": ["A", "B", "C", "D"], "extra_rel": [], "possible_solution": {"points": {"A": [-9.855769935618339, 9.810686703516286], "B": [9.994103013882478, -9.999547731193305], "C": [9.849871799244282, -9.853608241426931], "D": [-10.0, 9.956625126039908]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0015", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a kite with points A, B, C, D. There is a line segment AC. There is a line segment BD. There is a line segment EG. Line AC intersects line BD at point F. Line AC is perpendicular to line BD. Further, the length of line AC is equal to the length of line BD and the area of the kite is 12 square units.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\nkite1 = scene.add.kite(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EG = scene.add.line_segment(E, G)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_BD, F)\nscene.relate.perpendicular(line_AC, line_BD)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.eq(kite1.area, 12)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"kite1": "kite(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EG": "line_segment(E, G)"}, "Rels": ["lines_intersect_at(line_AC, line_BD, F)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.eq(scene.get_object('kite1').area, 12)"], "possible_solution": {"points": {"A": [-5.015203397973242, -2.956916569296592], "B": [-0.6989463383081554, -3.8609015399331175], "C": [-1.5167677351398066, 0.47250728440263706], "D": [-4.128370195113289, -0.3624658757640119], "E": [-1.672852788290062, 3.9377093193653914], "F": [-3.265985573767644, -1.2422046407571947], "G": [-1.5424619423862789, 5.439272241431899]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0016", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a triangle ABC. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment GH. Line AD is an altitude of triangle ABC from vertex A. Line BE is congruent to line CF. Further, the length of line AD equals the length of line BE and angle ABC is 60 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangle_ABC = scene.add.triangle(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_GH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.is_altitude(line_AD, triangle_ABC, A)\nscene.relate.congruent(line_BE, line_CF)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BE.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 60)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle_ABC": "Triangle(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_GH": "line_segment(G, H)"}, "Rels": ["is_altitude(line_AD, triangle_ABC, A)", "congruent(line_BE, line_CF)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 60)"], "possible_solution": {"points": {"A": [6.540166515544999, 4.337314324445799], "B": [-4.363923812523573, -6.072429328780653], "C": [-7.949513045672509, 8.668292892254673], "D": [-6.145452435492272, 1.2516162388080834], "E": [6.349488382218382, 1.3887542500531123], "F": [3.856093322052817, 3.09387634702601], "G": [-8.760332110128035, -4.408644886739804], "H": [-3.6552024423051503, -2.5990104938394154]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0017", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There are line segments BD and AC. Line BD is a diameter of the circle. Angle CAB is obtuse. Further, the length of line AC equals the length of line BD and angle CAB equals 120 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.obtuse_angle(C, A, B)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.eq(scene.angle(scene.get_object('C'), scene.get_object('A'), scene.get_object('B')), 120)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)"}, "Rels": ["is_diameter(line_BD, circle1)", "obtuse_angle(C, A, B)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.eq(scene.angle(scene.get_object('C'), scene.get_object('A'), scene.get_object('B')), 120)"], "possible_solution": {"points": {"A": [1.2776835189367957, -1.4096383549539446], "B": [3.928011662237005, 1.4446805349240062], "C": [-6.316470153281325, 0.32654580030520247], "D": [-1.372644632806159, -4.263957222648993]}, "circles": {"A": 3.8950449955601014}}}
{"unique_id": "1obj_2rel_2extra_gen0018", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a square with points A, B, C, D. There is a line segment AC. There is a line segment BD. There is a line segment EF. The square is congruent to itself. Line segment AC is perpendicular to line segment BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\nsquare1 = scene.add.square(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.congruent(square1, square1)\nscene.relate.perpendicular(line_AC, line_BD)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"square1": "square(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["congruent(square1, square1)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-10.0, -10.0], "B": [-10.0, 10.0], "C": [10.0, 10.0], "D": [10.0, -10.0], "E": [-7.578694970709665, -8.994915491451032], "F": [-2.033757227351379, -6.5689320080219]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0019", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a scalene triangle ABC. There is a line segment AD. There is a line segment BC. Line AD is an altitude of triangle ABC from vertex A. Point D lies on line BC. Further, length of line AD is equal to half the length of line BC, and the angle BAD is equal to 30 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ntriangleABC = scene.add.scalene_triangle(A, B, C)\nline_altitude_from_A = scene.add.line_segment(A, D)\nline_BC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude_from_A, triangleABC, A)\nscene.relate.point_lies_on(D, line_BC)\n\n### Extra relationships\n\nscene.constraint.eq(line_altitude_from_A.length, line_BC.length / 2)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 30)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "scalene_triangle(A, B, C)", "line_altitude_from_A": "line_segment(A, D)", "line_BC": "line_segment(B, C)"}, "Rels": ["is_altitude(line_altitude_from_A, triangleABC, A)", "point_lies_on(D, line_BC)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_altitude_from_A').length, scene.get_object('line_BC').length / 2)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 30)"], "possible_solution": {"points": {"A": [1.7368759087671983, 3.2069960816242267], "B": [-2.406085357009884, 0.8953450901006124], "C": [4.64930082932887, -3.317148021578153], "D": [-0.3693707552616771, -0.32069693823403045]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0020", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is an isosceles trapezoid ABCD. There is a line segment AD. There is a line segment BC. There is a line segment AC. There is a line segment BD. There is a line BD. The trapezoid ABCD is similar to itself. Line AD is perpendicular to line BC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ntrapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)\nline_AD = scene.add.line_segment(A, D)\nline_BC = scene.add.line_segment(B, C)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_m = scene.add.line(B, D)\n\n### relationships\n\nscene.relate.similar(trapezoid1, trapezoid1)\nscene.relate.perpendicular(line_AD, line_BC)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "isosceles_trapezoid(A, B, C, D)", "line_AD": "line_segment(A, D)", "line_BC": "line_segment(B, C)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_m": "line(B, D)"}, "Rels": ["similar(trapezoid1, trapezoid1)", "perpendicular(line_AD, line_BC)"], "Points": ["A", "B", "C", "D"], "extra_rel": [], "possible_solution": {"points": {"A": [9.932393306031743, -9.843041221026889], "B": [9.921373699842217, 9.983649093540638], "C": [-9.786831125153876, -9.746475418912334], "D": [-9.79773120661497, 9.865163604139296]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0023", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a trapezoid ABCD. There is a line segment AC. There is a line segment BD. There is a line segment AD. There is a line segment BC. The angle ADC is a right angle. Line AC is perpendicular to line BD. Further, the length of line AD equals the length of line BC and the angle ADC is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ntrapezoid1 = scene.add.trapezoid(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_AD = scene.add.line_segment(A, D)\nline_BC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.right_angle(A, D, C)\nscene.relate.perpendicular(line_AC, line_BD)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BC.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "trapezoid(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_AD": "line_segment(A, D)", "line_BC": "line_segment(B, C)"}, "Rels": ["right_angle(A, D, C)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BC').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [10.0, -10.0], "B": [-10.0, -10.0], "C": [-10.0, 10.0], "D": [10.0, 10.0]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0024", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a rectangle with vertices A, B, C, D. There is a line segment AC. There is a line segment BD. There is a line segment EF. Line segment AC intersects line segment BD at point G. Line segment AC is perpendicular to line segment BD. Further, the length of line segment AC is equal to the length of line segment BD. Further, the angle A G B is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_BD, G)\nscene.relate.perpendicular(line_AC, line_BD)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('G'), scene.get_object('B')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["lines_intersect_at(line_AC, line_BD, G)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('G'), scene.get_object('B')), 90)"], "possible_solution": {"points": {"A": [-0.6754986366183459, 1.4391086465265497], "B": [-1.8592606310925965, 1.4282513643584678], "C": [-1.8484033326029419, 0.24448937308097363], "D": [-0.664641363108158, 0.2553466776477248], "E": [0.4532555161497591, 2.014913428205853], "F": [-6.57033146141244, 9.164097708190225], "G": [-1.2619509983002382, 0.8417990070179435]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0025", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a rectangle ABCD. There are line segments AC, BD, and EF. Point E lies on line AC. Line AC is perpendicular to line BD. Further, length of line AC is equal to length of line BD and angle ABC is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.point_lies_on(E, line_AC)\nscene.relate.perpendicular(line_AC, line_BD)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["point_lies_on(E, line_AC)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [-8.277384500092321, -7.558088690447513], "B": [-8.155133444798926, 8.068559901481917], "C": [7.471515146897316, 7.946308846688297], "D": [7.349264092479376, -7.680339744904203], "E": [-7.958870681604305, -7.244519807729896], "F": [10.0, -10.0]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0026", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a minor arc with center A, start B, and end C. There are line segments AD and BE. Line AD is parallel to line BE. Point D lies on the minor arc. Further, the central angle of the minor arc is 90 degrees. Further, the length of line AD is less than or equal to the radius of the minor arc.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\narc1 = scene.add.minor_arc(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\n\n### relationships\n\nscene.relate.parallel(line_AD, line_BE)\nscene.relate.point_lies_on(D, arc1)\n\n### Extra relationships\n\nscene.constraint.eq(arc1.central_angle, 90)\nscene.constraint.leq(line_AD.length, arc1.radius)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"arc1": "minor_arc(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)"}, "Rels": ["parallel(line_AD, line_BE)", "point_lies_on(D, arc1)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('arc1').central_angle, 90)", "scene.constraint.leq(scene.get_object('line_AD').length, scene.get_object('arc1').radius)"], "possible_solution": {"points": {"A": [3.373615405702066, 2.628746982841596], "B": [0.057775659518840956, 2.7584404773927513], "C": [3.2439219129901185, -0.6870927698208451], "D": [0.4870431150255455, 0.9918859665896387], "E": [-0.4182523174014597, 2.4885038494286364]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0027", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a rectangle with vertices A, B, C, D. There is a line segment AC. There is a line segment BD. There is a line segment EF. G is the centroid of the rectangle. Line AC is perpendicular to line BD. Further, length of line AC is equal to length of line BD and the angle at G between points A and B is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_centroid(G, rectangle1)\nscene.relate.perpendicular(line_AC, line BD)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, 'line BD'.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('G'), scene.get_object('B')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "line_AC": "line_segment(A, C)", "line BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["is_centroid(G, rectangle1)", "perpendicular(line_AC, line BD)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line BD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('G'), scene.get_object('B')), 90)"], "possible_solution": {"points": {"A": [0.7791047180280711, 6.802579866551449], "B": [1.7103311650376773, 6.390899776786419], "C": [1.2986510683357793, 5.459673321352161], "D": [0.36742461274994337, 5.8713534105877345], "E": [-9.579797848878755, -3.145867470738987], "F": [0.20878249715102015, -4.312191249259081], "G": [1.0388778999561827, 6.131126594848348]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0029", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a triangle with points A, B, C. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment GH. Line AD is an altitude of triangle ABC from vertex A. Line BE is parallel to line CF. Further, the length of line BE is equal to the length of line CF. Further, angle BAC is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangle_ABC = scene.add.triangle(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_GH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.is_altitude(line_AD, triangle_ABC, A)\nscene.relate.parallel(line_BE, line_CF)\n\n### Extra relationships\n\nscene.constraint.eq(line_BE.length, line_CF.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle_ABC": "triangle(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_GH": "line_segment(G, H)"}, "Rels": ["is_altitude(line_AD, triangle_ABC, A)", "parallel(line_BE, line_CF)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_BE').length, scene.get_object('line_CF').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [-0.6386669511719257, -3.466548454061487], "B": [1.7055923355561942, -0.13357703585680686], "C": [-8.699451857787647, 2.2030380947742554], "D": [0.18641552418782495, 0.20757799216496436], "E": [2.604482636970844, -1.7685424360802395], "F": [-7.8005615401884745, 0.5680725906874338], "G": [-2.255505700171101, -2.666758597342278], "H": [-1.7729486415528493, -4.857259802174125]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0030", "nl_description": "Diagram description: The diagram contains points A, B, C, D, M, N. There is an isosceles trapezoid ABCD. There are line segments AC, BD, and MN. Points A, M and B are collinear. Line AC is perpendicular to line BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, M, N = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"M\", \"N\"])\n\ntrapezoid_ABCD = scene.add.isosceles_trapezoid(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_MN = scene.add.line_segment(M, N)\n\n### relationships\n\nscene.relate.collinear(A, M, B)\nscene.relate.perpendicular(line_AC, line_BD)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid_ABCD": "isosceles_trapezoid(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_MN": "line_segment(M, N)"}, "Rels": ["collinear(A, M, B)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "M", "N"], "extra_rel": [], "possible_solution": {"points": {"A": [0.7413493883019208, 1.1134475012581542], "B": [1.2424551191667808, -0.03405101113298578], "C": [1.0488394774196004, 1.8976912240382753], "D": [2.0266988433050077, -0.34154111127167447], "M": [1.1606710999922158, 0.15322892383610723], "N": [6.987962243672235, -7.0420306597333475]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0032", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is an obtuse triangle ABC. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is an altitude of triangle ABC from vertex A. Line BE is an altitude of triangle ABC from vertex B. Line AD is congruent to line BE. Further, the length of line AD equals the length of line BE and angle ABC measures 120 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ntriangleABC = scene.add.obtuse_triangle(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_altitude(line_AD, triangleABC, A)\nscene.relate.congruent(line_AD, line_BE)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BE.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 120)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "obtuse_triangle(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["is_altitude(line_AD, triangleABC, A)", "congruent(line_AD, line_BE)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 120)"], "possible_solution": {"points": {"A": [-4.434142607145419, -4.556557377780006], "B": [2.168257131465609, 2.3037055107211177], "C": [9.971880953075082, 0.37211448820212434], "D": [-2.452923747449183, 3.4475628262588307], "E": [-0.8416199031906879, -5.373000001915358], "F": [-10.0, -8.052166661752063]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0034", "nl_description": "Diagram description: The diagram contains points A, B, C, H. There is a right triangle with vertices A, B, C. There is a line segment BH. There is a line segment AC. There is a line segment AB. Line BH is an altitude of triangle ABC from vertex B. Angle ABH is acute.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, H = scene.add.points([\"A\", \"B\", \"C\", \"H\"])\n\ntriangleABC = scene.add.right_triangle(A, B, C)\nlineBH = scene.add.line_segment(B, H)\nlineAC = scene.add.line_segment(A, C)\nlineAB = scene.add.line_segment(A, B)\n\n### relationships\n\nscene.relate.is_altitude(lineBH, triangleABC, B)\nscene.relate.acute_angle(A, B, H)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "right_triangle(A, B, C)", "lineBH": "line_segment(B, H)", "lineAC": "line_segment(A, C)", "lineAB": "line_segment(A, B)"}, "Rels": ["is_altitude(lineBH, triangleABC, B)", "acute_angle(A, B, H)"], "Points": ["A", "B", "C", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [4.608540928769434, 0.492050799222289], "B": [3.740548822103228, 1.1950899848265304], "C": [4.27038393046144, 1.8492394243593353], "H": [4.392874908918001, 1.3576234957403224]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0035", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a square with A, B, C, D. There is a line segment AC. There is a line segment BD. There is a line segment EF. Points A, E, and C are collinear. Line segment AC is perpendicular to line segment BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\nsquare1 = scene.add.square(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.collinear(A, E, C)\nscene.relate.perpendicular(line_AC, line_BD)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"square1": "square(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["collinear(A, E, C)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.17263328984104034, 5.508934203634808], "B": [-3.8736845045702832, 7.050482491868876], "C": [-5.41523279287825, 3.3494312757633713], "D": [-1.7141815769923412, 1.8078829871306645], "E": [-1.7900742178876847, 4.842686781644847], "F": [6.7141746470972885, 5.335031636643116]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0038", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a major arc BC with center A. There is a line segment DE. There is a line segment CF. The extensions of line segment DE and line segment CF intersect at point G. Point F lies on the major arc BC with center A.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\nmajor_arc1 = scene.add.major_arc(A, B, C)\nline_DE = scene.add.line_segment(D, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line_DE, line_CF, G)\nscene.relate.point_lies_on(F, major_arc1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"major_arc1": "major_arc(A, B, C)", "line_DE": "line_segment(D, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["line_extensions_intersect_at(line_DE, line_CF, G)", "point_lies_on(F, major_arc1)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.999539726681705, -1.3920064404335952], "B": [-0.26479878391893863, -3.627034672143572], "C": [0.9752780109964373, -2.670791156285299], "D": [3.561060428328358, 2.303592337203832], "E": [3.18933155611469, 1.8509088555168507], "F": [-2.9003284610682525, -0.005573013891784218], "G": [0.017260498697295804, -2.011971516957197]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0040", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is an obtuse triangle ABC with vertices A, B, C. There is a line segment AD. There is a line segment BE. Line AD is an altitude of triangle ABC from vertex A. Line AD and line BE intersect at point D.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ntriangleABC = scene.add.obtuse_triangle(A, B, C)\nline_altitude = scene.add.line_segment(A, D)\nline_perpendicular = scene.add.line_segment(B, E)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude, triangleABC, A)\nscene.relate.lines_intersect_at(line_altitude, line_perpendicular, D)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "obtuse_triangle(A, B, C)", "line_altitude": "line_segment(A, D)", "line_perpendicular": "line_segment(B, E)"}, "Rels": ["is_altitude(line_altitude, triangleABC, A)", "lines_intersect_at(line_altitude, line_perpendicular, D)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [0.5220201328771029, 1.7448063056870065], "B": [1.4431176715577059, -0.07337112154315495], "C": [-6.453835390945844, -8.491581665398956], "D": [1.9192019590468508, 0.4341382588596753], "E": [4.002783321126034, 2.655251444443609]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0041", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is an isosceles trapezoid ABCD. There is a line segment AC. There is a line segment BD. There is a line BD. The trapezoid ABCD is congruent to itself. The trapezoid ABCD is a mirror image of itself across line BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ntrapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_m = scene.add.line(B, D)\n\n### relationships\n\nscene.relate.congruent(trapezoid1, trapezoid1)\nscene.relate.mirror_across_line(trapezoid1, trapezoid1, line_m)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "isosceles_trapezoid(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_m": "line(B, D)"}, "Rels": ["congruent(trapezoid1, trapezoid1)", "mirror_across_line(trapezoid1, trapezoid1, line_m)"], "Points": ["A", "B", "C", "D"], "extra_rel": [], "possible_solution": {"points": {"A": [-2.616683196119324, 2.696712280602397], "B": [-9.6482939323826, 9.095409862945417], "C": [2.968403100828018, -2.3800329568918115], "D": [10.0, -8.778717701972782]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0043", "nl_description": "Diagram description: The diagram contains points O, A, B, P. There is a major arc with center O, start point A, end point B. There is a line segment OP. There is a line segment OA. The line OP is a rotation of line OA around point O by 90 degrees. Point P lies on the major arc. Further, length of line OA is equal to length of line OP and angle AOP is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nO, A, B, P = scene.add.points([\"O\", \"A\", \"B\", \"P\"])\n\nsemicircle1 = scene.add.major_arc(O, A, B)\nline_OP = scene.add.line_segment(O, P)\nline_OA = scene.add.line_segment(O, A)\n\n### relationships\n\nscene.relate.rotation_around_point(line_OA, line_OP, O, 90)\nscene.relate.point_lies_on(P, semicircle1)\n\n### Extra relationships\n\nscene.constraint.eq(line_OA.length, line_OP.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('O'), scene.get_object('P')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"semicircle1": "major_arc(O, A, B)", "line_OP": "line_segment(O, P)", "line_OA": "line_segment(O, A)"}, "Rels": ["rotation_around_point(line_OA, line_OP, O, 90)", "point_lies_on(P, semicircle1)"], "Points": ["O", "A", "B", "P"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_OA').length, scene.get_object('line_OP').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('O'), scene.get_object('P')), 90)"], "possible_solution": {"points": {"O": [-2.930539580859558, -4.068670363898623], "A": [-5.2666124079394185, -1.2535487503663938], "B": [0.6448892444753728, -4.842268874764719], "P": [-0.11541796731604911, -1.7325975361559471]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0045", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a parallelogram ABCD. There is a line segment AC. There is a line segment BD. There is a line segment EF. The parallelogram ABCD is similar to itself. Line segment AC is perpendicular to line segment BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\nparallelogram1 = scene.add.parallelogram(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.similar(parallelogram1, parallelogram1)\nscene.relate.perpendicular(line_AC, line_BD)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"parallelogram1": "parallelogram(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["similar(parallelogram1, parallelogram1)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [10.0, 10.0], "B": [-10.0, 10.0], "C": [-10.0, -10.0], "D": [10.0, -10.0], "E": [1.4043378937989797, -7.77248026664982], "F": [-0.8809982155721443, 3.3372776598264187]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0048", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a major arc with center A, start point B, end point C. There is a line segment AD. There is a line segment BE. There is a line segment CD. Line AD intersects line BE at D. Point D lies on the major arc.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nsemicircle1 = scene.add.major_arc(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CD = scene.add.line_segment(C, D)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AD, line_BE, D)\nscene.relate.point_lies_on(D, semicircle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"semicircle1": "major_arc(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CD": "line_segment(C, D)"}, "Rels": ["lines_intersect_at(line_AD, line_BE, D)", "point_lies_on(D, semicircle1)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [0.9207802149045482, -0.29976571934511287], "B": [1.1716982081293, 0.5369711512032332], "C": [1.5199970028391998, -0.9353974238426882], "D": [1.7743521707871246, -0.4855164790941949], "E": [1.8785471428703926, -0.6622979640168023]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0049", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a kite with points A, B, C, D. There is a line segment AC. There is a line segment BD. There is a line segment BE. Line AC is perpendicular to line BD. Line BE is the angle bisector of angle ABD. Further, the length of line AC is equal to the length of line BD and the angle ABD measures 45 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nkite1 = scene.add.kite(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_angle_bisector = scene.add.line_segment(B, E)\n\n### relationships\n\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.angle_bisector(A, B, D, line_angle_bisector)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('D')), 45)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"kite1": "kite(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_angle_bisector": "line_segment(B, E)"}, "Rels": ["perpendicular(line_AC, line_BD)", "angle_bisector(A, B, D, line_angle_bisector)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('D')), 45)"], "possible_solution": {"points": {"A": [5.159547327291583, -5.498226713220247], "B": [-7.995278012763012, -5.303671912500591], "C": [-7.800723219636029, 7.851153440808459], "D": [5.354102175883411, 7.656598667740191], "E": [6.539963140905474, 0.46670183910397356]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0052", "nl_description": "Diagram description: The diagram contains points A, B, O, P, Q. There is a major arc with center O from A to B. There is a line segment PQ. There is a line segment AB. Line PQ intersects line AB at O. Point P lies on the major arc from A to B centered at O. Further, the radius of the major arc is 3.0. Further, the angle POA is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, O, P, Q = scene.add.points([\"A\", \"B\", \"O\", \"P\", \"Q\"])\n\nsemicircle1 = scene.add.major_arc(O, A, B)\nline_perp = scene.add.line_segment(P, Q)\nline_base = scene.add.line_segment(A, B)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_perp, line_base, O)\nscene.relate.point_lies_on(P, semicircle1)\n\n### Extra relationships\n\nscene.constraint.eq(semicircle1.radius, 3.0)\nscene.constraint.eq(scene.angle(scene.get_object('P'), scene.get_object('O'), scene.get_object('A')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"semicircle1": "major_arc(O, A, B)", "line_perp": "line_segment(P, Q)", "line_base": "line_segment(A, B)"}, "Rels": ["lines_intersect_at(line_perp, line_base, O)", "point_lies_on(P, semicircle1)"], "Points": ["A", "B", "O", "P", "Q"], "extra_rel": ["scene.constraint.eq(scene.get_object('semicircle1').radius, 3.0)", "scene.constraint.eq(scene.angle(scene.get_object('P'), scene.get_object('O'), scene.get_object('A')), 90)"], "possible_solution": {"points": {"A": [0.05470647726867829, 0.056472932567216916], "B": [-5.583886873027769, -1.994444970980766], "O": [-2.764590183281365, -0.9689860431134057], "P": [-1.7391312010946798, -3.7882827151346707], "Q": [-3.5930091636081984, 1.3085881153397831]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0053", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a kite with points A, B, C, D. There is a line segment AC. There is a line segment BD. There is a line segment EF. Line AC is perpendicular to line BD. Line BD is parallel to line EF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\nkite1 = scene.add.kite(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.parallel(line_BD, line_EF)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"kite1": "kite(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["perpendicular(line_AC, line_BD)", "parallel(line_BD, line_EF)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-7.177973658049178, -3.304653506287333], "B": [-1.0003651549567492, 4.580800202271219], "C": [-4.26768933957482, -4.888509154273293], "D": [-0.9046571194858715, 4.7566606567295215], "E": [-7.217303408143651, -6.572923286625139], "F": [-5.967611771351512, -4.276654971880976]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0054", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G.\nThere is an acute triangle ABC.\nThere is a line segment AD.\nThere is a line segment EF.\nLine AD is an altitude of triangle ABC from vertex A.\nThe extensions of line AD and line EF intersect at point G.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntriangleABC = scene.add.acute_triangle(A, B, C)\nline_altitude_from_A = scene.add.line_segment(A, D)\nline_perpendicular_bisector = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude_from_A, triangleABC, A)\nscene.relate.line_extensions_intersect_at(line_altitude_from_A, line_perpendicular_bisector, G)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "acute_triangle(A, B, C)", "line_altitude_from_A": "line_segment(A, D)", "line_perpendicular_bisector": "line_segment(E, F)"}, "Rels": ["is_altitude(line_altitude_from_A, triangleABC, A)", "line_extensions_intersect_at(line_altitude_from_A, line_perpendicular_bisector, G)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [-3.1771130146222313, -2.365654978446316], "B": [5.708074578814536, 3.565929419320149], "C": [9.01401540730192, 8.015020247955714], "D": [-0.2922758487248936, -4.509261724442906], "E": [3.3698787703990742, 1.2852646124703744], "F": [1.8793931135874837, -0.8870944856114507], "G": [-0.4999491946215356, -4.354947996184804]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0055", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a parallelogram ABCD. There is a line segment AC. There is a line segment BD. There is a line segment EF. Point E lies on line AC. Line AC is perpendicular to line BD. Further, length of line AC is equal to length of line BD and angle AEB is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\nparallelogram1 = scene.add.parallelogram(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.point_lies_on(E, line_AC)\nscene.relate.perpendicular(line_AC, line_BD)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('E'), scene.get_object('B')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"parallelogram1": "parallelogram(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["point_lies_on(E, line_AC)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('E'), scene.get_object('B')), 90)"], "possible_solution": {"points": {"A": [5.248998219470667, -7.165749797169181], "B": [5.754366304906647, 7.248758806974441], "C": [-8.660142297930477, 7.754126855653546], "D": [-9.165510396600714, -6.660381760961907], "E": [-1.7055720025221905, 0.29418848603760517], "F": [2.3955174836940585, -2.4289168855807146]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0056", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a triangle ABC. There is a line segment AD. There is a line segment DE. Line AD is an altitude of triangle ABC from vertex A. Line AD is perpendicular to line DE.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\nline_altitude = scene.add.line_segment(A, D)\nline_perpendicular = scene.add.line_segment(D, E)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude, triangleABC, A)\nscene.relate.perpendicular(line_altitude, line_perpendicular)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "Triangle(A, B, C)", "line_altitude": "line_segment(A, D)", "line_perpendicular": "line_segment(D, E)"}, "Rels": ["is_altitude(line_altitude, triangleABC, A)", "perpendicular(line_altitude, line_perpendicular)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [-1.5343769102707776, -0.3493698763917002], "B": [6.970465447723851, -3.1615544442478036], "C": [-5.609227250334944, -1.3116800024248167], "D": [-1.759142786009637, -1.8778443077565667], "E": [-2.5096999123801758, -1.7674730622225385]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0057", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a right trapezoid ABCD with AB parallel to CD and right angles at A and D. There are line segments AC, BD, and EF. Points A, E, and F are collinear. Lines AC and BD intersect at point G. Further, the length of line AC is equal to the length of line BD. Further, angle AGB is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntrapezoidABCD = scene.add.right_trapezoid(A, B, C, D)\nlineAC = scene.add.line_segment(A, C)\nlineBD = scene.add.line_segment(B, D)\nlineEF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.collinear(A, E, F)\nscene.relate.lines_intersect_at(lineAC, lineBD, G)\n\n### Extra relationships\n\nscene.constraint.eq(lineAC.length, lineBD.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('G'), scene.get_object('B')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoidABCD": "right_trapezoid(A, B, C, D)", "lineAC": "line_segment(A, C)", "lineBD": "line_segment(B, D)", "lineEF": "line_segment(E, F)"}, "Rels": ["collinear(A, E, F)", "lines_intersect_at(lineAC, lineBD, G)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('lineAC').length, scene.get_object('lineBD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('G'), scene.get_object('B')), 90)"], "possible_solution": {"points": {"A": [0.5514263316315798, 0.825562666318535], "B": [0.08958793661114893, -1.4327106628966173], "C": [-2.1686849916794415, -0.9708719932639043], "D": [-1.706846741142199, 1.287400842697949], "E": [0.20913137981336835, 0.2831120210312559], "F": [-0.8187747712406073, -1.3458590323194153], "G": [-0.8086294394144949, -0.07265441252989913]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0060", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a triangle with vertices A, B, C. There are line segments AD, BE, and BC. AD is an altitude of triangle ABC from vertex A. AD and BE intersect at point A. Further, the length of line BC is equal to the length of line BE and angle ABD is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\nline_altitude = scene.add.line_segment(A, D)\nline_perpendicular = scene.add.line_segment(B, E)\nline_base = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude, triangleABC, A)\nscene.relate.lines_intersect_at(line_altitude, line_perpendicular, A)\n\n### Extra relationships\n\nscene.constraint.eq(line_base.length, line_perpendicular.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "line_altitude": "line_segment(A, D)", "line_perpendicular": "line_segment(B, E)", "line_base": "line_segment(B, C)"}, "Rels": ["is_altitude(line_altitude, triangleABC, A)", "lines_intersect_at(line_altitude, line_perpendicular, A)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_base').length, scene.get_object('line_perpendicular').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 90)"], "possible_solution": {"points": {"A": [4.478080600746556, -0.571155374597999], "B": [-9.99968690443868, 8.600111177974055], "C": [5.501544158311909, -0.9666369694801914], "D": [4.585626030799536, -0.40138434968445885], "E": [5.388341029508323, -1.147775441379781]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0061", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a line segment BC. There is a line segment DE. There is a line FG. Line BC intersects line DE at point H. Line BC is a chord of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ncircle1 = scene.add.circle(A)\nline1 = scene.add.line_segment(B, C)\nline2 = scene.add.line_segment(D, E)\nline3 = scene.add.line(F, G)\n\n### relationships\n\nscene.relate.lines_intersect_at(line1, line2, H)\nscene.relate.is_chord(line1, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line1": "line_segment(B, C)", "line2": "line_segment(D, E)", "line3": "line(F, G)"}, "Rels": ["lines_intersect_at(line1, line2, H)", "is_chord(line1, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [-1.357805748178243, -0.7780893800193557], "B": [-1.4592290666869379, 1.5206181226030817], "C": [0.26426025089778477, -2.410034459330169], "D": [-3.0447474902085165, -1.9168789916347713], "E": [-0.5716334374656267, 0.998427066710021], "F": [-6.230659271634124, 3.591841324299339], "G": [-8.961643702380618, -5.201143122535794], "H": [-1.0058348035774434, 0.4865906305499705]}, "circles": {"A": 2.3009439044621733}}}
{"unique_id": "1obj_2rel_2extra_gen0064", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is an equilateral triangle ABC. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment GH. Line AD is an altitude of triangle ABC from vertex A. The extensions of line AD and line BE intersect at point F. Point G is the centroid of triangle ABC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangleABC = scene.add.equilateral_triangle(A, B, C)\nlineAD = scene.add.line_segment(A, D)\nlineBE = scene.add.line_segment(B, E)\nlineCF = scene.add.line_segment(C, F)\nlineGH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.is_altitude(lineAD, triangleABC, A)\nscene.relate.line_extensions_intersect_at(lineAD, lineBE, F)\nscene.relate.is_centroid(G, triangleABC)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "equilateral_triangle(A, B, C)", "lineAD": "line_segment(A, D)", "lineBE": "line_segment(B, E)", "lineCF": "line_segment(C, F)", "lineGH": "line_segment(G, H)"}, "Rels": ["is_altitude(lineAD, triangleABC, A)", "line_extensions_intersect_at(lineAD, lineBE, F)", "is_centroid(G, triangleABC)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [1.759624981369398, 4.305513946754342], "B": [-0.4148059103463592, -2.91578423319927], "C": [-5.581418152634086, 2.5779771866314167], "D": [-2.9981119899396886, -0.16890360396076914], "E": [-3.1944874107837733, 1.547163070256603], "F": [-2.4479282841848944, 0.3485170988460629], "G": [-1.4121996234825986, 1.3225689620154633], "H": [8.731543227491803, -4.441781478754535]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0066", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is an obtuse triangle ABC with vertices A, B, C. There are line segments AD and EF. Line AD is an altitude of triangle ABC from vertex A. Point G is the centroid of triangle ABC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntriangleABC = scene.add.obtuse_triangle(A, B, C)\nline_altitude_from_A = scene.add.line_segment(A, D)\nline_perpendicular_bisector = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude_from_A, triangleABC, A)\nscene.relate.is_centroid(G, triangleABC)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "obtuse_triangle(A, B, C)", "line_altitude_from_A": "line_segment(A, D)", "line_perpendicular_bisector": "line_segment(E, F)"}, "Rels": ["is_altitude(line_altitude_from_A, triangleABC, A)", "is_centroid(G, triangleABC)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [-3.892280565959386, 2.158060916538472], "B": [4.417980848844999, -6.241084680968213], "C": [-2.714403448831709, 6.04299068564436], "D": [-1.324413481873175, 3.649016834696844], "E": [-7.172553710154507, 1.103720681083276], "F": [-4.210498822844516, -9.949813669194468], "G": [-0.729567723265476, 0.6533223050380444]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0067", "nl_description": "Diagram description: The diagram contains points A, B, C, D, O. There is an isosceles trapezoid ABCD. There is a line segment AC. There is a line segment BD. There is a line CD. Line AC and line BD intersect at point O. Line CD is perpendicular to line AC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, O = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"O\"])\n\ntrapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_m = scene.add.line(C, D)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_BD, O)\nscene.relate.perpendicular(line_m, line_AC)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "isosceles_trapezoid(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_m": "line(C, D)"}, "Rels": ["lines_intersect_at(line_AC, line_BD, O)", "perpendicular(line_m, line_AC)"], "Points": ["A", "B", "C", "D", "O"], "extra_rel": [], "possible_solution": {"points": {"A": [-3.768143660787897, 2.859184818328574], "B": [-2.763858136444334, 4.128724458037862], "C": [-2.255024614864737, 1.6622127648304659], "D": [-3.25931008660311, 0.3926731107273515], "O": [-3.0115841118201314, 2.260698848473964]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0068", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is an acute triangle ABC. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment GH. Line AD is an altitude of triangle ABC from vertex A. Line BE is an altitude of triangle ABC from vertex B. Point F is the orthocenter of triangle ABC. Line AD is the mirror image of line BE across line GH. Line AD is congruent to line BE.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangleABC = scene.add.acute_triangle(A, B, C)\nlineAD = scene.add.line_segment(A, D)\nlineBE = scene.add.line_segment(B, E)\nlineCF = scene.add.line_segment(C, F)\nlineGH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.is_altitude(lineAD, triangleABC, A)\nscene.relate.is_altitude(lineBE, triangleABC, B)\nscene.relate.is_orthocenter(F, triangleABC)\nscene.relate.mirror_across_line(lineAD, lineBE, lineGH)\nscene.relate.congruent(lineAD, lineBE)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "acute_triangle(A, B, C)", "lineAD": "line_segment(A, D)", "lineBE": "line_segment(B, E)", "lineCF": "line_segment(C, F)", "lineGH": "line_segment(G, H)"}, "Rels": ["is_altitude(lineAD, triangleABC, A)", "is_altitude(lineBE, triangleABC, B)", "is_orthocenter(F, triangleABC)", "mirror_across_line(lineAD, lineBE, lineGH)", "congruent(lineAD, lineBE)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [4.982998135937399, -6.15462310850928], "B": [4.082777373238633, 2.701688228633414], "C": [-1.1823755421315607, -2.3074085437365417], "D": [0.13265088173253628, -1.0563351339844345], "E": [0.3574902738917978, -3.268290131769657], "F": [1.1019761143751317, -2.0752101532759486], "G": [-5.993144422597942, -2.7964106364312245], "H": [9.280335057984091, -1.2439019558036586]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0073", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a right triangle with vertices A, B, C. There is a line segment BD. There is a line segment CE. There is a line segment AF. Line BD is congruent to line CE. Line BD is an altitude of triangle ABC from vertex B. Further, length of line BD equals length of line CE. Further, angle ABC equals 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ntriangleABC = scene.add.right_triangle(A, B, C)\nlineBD = scene.add.line_segment(B, D)\nlineCE = scene.add.line_segment(C, E)\nlineAF = scene.add.line_segment(A, F)\n\n### relationships\n\nscene.relate.congruent(lineBD, lineCE)\nscene.relate.is_altitude(lineBD, triangleABC, B)\n\n### Extra relationships\n\nscene.constraint.eq(lineBD.length, lineCE.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "right_triangle(A, B, C)", "lineBD": "line_segment(B, D)", "lineCE": "line_segment(C, E)", "lineAF": "line_segment(A, F)"}, "Rels": ["congruent(lineBD, lineCE)", "is_altitude(lineBD, triangleABC, B)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('lineBD').length, scene.get_object('lineCE').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [0.9834981943369476, -1.1293401673471812], "B": [-1.8803338002071706, -2.550854962137317], "C": [-2.8523570015285142, -0.5925839966494701], "D": [-1.6302403626249022, -0.7635963795655811], "E": [-4.504327674161942, -1.319105057976302], "F": [-5.157506176949566, -6.201940985088331]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0074", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a triangle ABC. There is a line segment AD. There is a line segment BE. There is a line BD. There is a line AE. Line AD is an altitude of triangle ABC from A. Line BE is a median of triangle ABC from B. Line BD and line AE intersect at point F.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\nline_altitude = scene.add.line_segment(A, D)\nline_median = scene.add.line_segment(B, E)\nline_extension1 = scene.add.line(B, D)\nline_extension2 = scene.add.line(A, E)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude, triangleABC, A)\nscene.relate.is_median(line_median, triangleABC, B)\nscene.relate.line_extensions_intersect_at(line_extension1, line_extension2, F)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "line_altitude": "line_segment(A, D)", "line_median": "line_segment(B, E)", "line_extension1": "line(B, D)", "line_extension2": "line(A, E)"}, "Rels": ["is_altitude(line_altitude, triangleABC, A)", "is_median(line_median, triangleABC, B)", "line_extensions_intersect_at(line_extension1, line_extension2, F)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [2.6412548366084976, -6.323468341901162], "B": [2.8813619040069796, -5.845036313559435], "C": [-4.981611652596896, 3.2000899065946604], "D": [3.0150103745677947, -5.998566050475233], "E": [-1.1701897965388386, -1.5617352494339694], "F": [-4.856473304950825, 3.0436187774500336]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0077", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a parallelogram ABCD. There is a line segment AC. There is a line segment BD. There is a line segment EF. Point E lies on line AC. Line AC is perpendicular to line BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\nparallelogram1 = scene.add.parallelogram(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.point_lies_on(E, line_AC)\nscene.relate.perpendicular(line_AC, line_BD)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"parallelogram1": "parallelogram(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["point_lies_on(E, line_AC)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-1.6541782590500116, 2.861703211753047], "B": [1.7918332855049226, 1.621831994340599], "C": [1.254090530139433, -2.00075118665589], "D": [-2.1919210122177284, -0.7608799728664513], "E": [-0.5795324652974252, 1.0649586412190695], "F": [-3.4901648909899357, -7.083542589261082]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0078", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is an isosceles trapezoid ABCD. There is a line segment AC. There is a line segment BD. There is a line BC. A, D, and C are collinear. Line AC intersects line BD at E.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ntrapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_m = scene.add.line(B, C)\n\n### relationships\n\nscene.relate.collinear(A, D, C)\nscene.relate.lines_intersect_at(line_AC, line_BD, E)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "isosceles_trapezoid(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_m": "line(B, C)"}, "Rels": ["collinear(A, D, C)", "lines_intersect_at(line_AC, line_BD, E)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [-8.765982421426475, 8.777485885386364], "B": [-8.621553505070501, 8.633826852630444], "C": [9.083919784273016, -9.52989319566241], "D": [8.941719674947386, -9.384060793137982], "E": [8.801983935653178, -9.240720415118808]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0080", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is an obtuse triangle ABC. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD intersects line BE at G. Line AD is an altitude of triangle ABC from vertex A. Line BE is an altitude of triangle ABC from vertex B. Line CF is an altitude of triangle ABC from vertex C.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntriangleABC = scene.add.obtuse_triangle(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AD, line_BE, G)\nscene.relate.is_altitude(line_AD, triangleABC, A)\nscene.relate.is_altitude(line_BE, triangleABC, B)\nscene.relate.is_altitude(line_CF, triangleABC, C)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "obtuse_triangle(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["lines_intersect_at(line_AD, line_BE, G)", "is_altitude(line_AD, triangleABC, A)", "is_altitude(line_BE, triangleABC, B)", "is_altitude(line_CF, triangleABC, C)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [1.3036899684967638, 0.5101539689437814], "B": [5.560074918293221, 0.1993367604097146], "C": [1.5610516459060837, -6.846279831081471], "D": [4.656389868389485, -1.3928062430536616], "E": [1.3197538160600233, 0.05099067196802381], "F": [2.0940316772749767, 0.4524402612619412], "G": [2.0666246194988656, 0.07711966254184895]}, "circles": {}}}
{"unique_id": "1obj_2rel_2extra_gen0081", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a rectangle with points A, B, C, D. There is a line segment AC. There is a line segment BD. There is a line segment EF. Point G is the midpoint of line AC. Line AC is perpendicular to line BD. Further, the length of line AC is equal to the length of line BD. Further, the slope of line AC is the negative reciprocal of the slope of line BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_midpoint(G, line_AC)\nscene.relate.perpendicular(line_AC, line_BD)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.eq(line_AC.slope, -1 * line_BD.slope)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["is_midpoint(G, line_AC)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.eq(scene.get_object('line_AC').slope, -1 * scene.get_object('line_BD').slope)"], "possible_solution": {"points": {"A": [-0.2298271310140238, -0.2035700717372881], "B": [-0.22982714362357984, -0.9382734485769022], "C": [-0.9645308752791998, -0.938273503449432], "D": [-0.9645308661407944, -0.20357012703813415], "E": [-9.160399620774111, 9.221658238757588], "F": [-3.9224774091207104, 2.9796455893146785], "G": [-0.5971789863684716, -0.5709217807984105]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0003", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a triangle ABC. There is a triangle DEF. There is a line segment AD. There is a line segment BE. There is a line segment CF. Triangle ABC is similar to triangle DEF. Line AD is an altitude of triangle ABC from vertex A. Line BE is an altitude of triangle ABC from vertex B.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ntriangle_ABC = scene.add.triangle(A, B, C)\ntriangle_DEF = scene.add.triangle(D, E, F)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.similar(triangle_ABC, triangle_DEF)\nscene.relate.is_altitude(line_AD, triangle_ABC, A)\nscene.relate.is_altitude(line_BE, triangle_ABC, B)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle_ABC": "triangle(A, B, C)", "triangle_DEF": "triangle(D, E, F)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["similar(triangle_ABC, triangle_DEF)", "is_altitude(line_AD, triangle_ABC, A)", "is_altitude(line_BE, triangle_ABC, B)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.19202025534427675, 2.6170921332249417], "B": [0.29988125298390966, 1.979693153439412], "C": [0.4584092643612516, 6.751842827225148], "D": [0.320485520976454, 2.6000705796534165], "E": [-0.2779751073327391, 2.070601786159599], "F": [4.458042228726155, 2.2309060418189244]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0011", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a trapezoid ABCD. There is a line segment AC. There is a line segment BD. There is a line segment AD. There is a line segment BC. There is a line segment CD. There is a line segment AB. Angle BAD is a right angle. Line AC is perpendicular to line BD. Point E is the midpoint of line AB. Further, length of line AD equals length of line BC, the slope of line AB is less than or equal to 0, and angle ABC is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ntrapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_AD = scene.add.line_segment(A, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_AB = scene.add.line_segment(A, B)\n\n### relationships\n\nscene.relate.right_angle(B, A, D)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.is_midpoint(E, line_AB)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BC.length)\nscene.constraint.leq(line_AB.slope, 0)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "isosceles_trapezoid(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_AD": "line_segment(A, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_AB": "line_segment(A, B)"}, "Rels": ["right_angle(B, A, D)", "perpendicular(line_AC, line_BD)", "is_midpoint(E, line_AB)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BC').length)", "scene.constraint.leq(scene.get_object('line_AB').slope, 0)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [-5.939960684907608, -3.5574396869239404], "B": [6.369625658323289, -3.7842531979679204], "C": [6.596439204794856, 8.52533313337637], "D": [-5.713147215218085, 8.7521467011418], "E": [0.2148329660416062, -3.6708463516945624]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0016", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a line segment BD. There is a line segment AC. Line BD is a diameter of the circle with center A. Line BD is perpendicular to line AC. The extensions of lines BD and AC intersect at point A.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\nscene.relate.line_extensions_intersect_at(line_BD, line_AC, A)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)"}, "Rels": ["is_diameter(line_BD, circle1)", "perpendicular(line_BD, line_AC)", "line_extensions_intersect_at(line_BD, line_AC, A)"], "Points": ["A", "B", "C", "D"], "extra_rel": [], "possible_solution": {"points": {"A": [0.12597739492806181, 1.024416318405458], "B": [1.2472113756088243, -0.7275135515215714], "C": [2.2557782763186918, 2.3874874996111615], "D": [-0.9952565838110585, 2.7763461870442017]}, "circles": {"A": 2.080005744131787}}}
{"unique_id": "1obj_3rel_3extra_gen0018", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There is a line segment BD. There is a line segment AC. There is a line segment EF. BD is a diameter of the circle. BD is perpendicular to line AC. The extension of line EF intersects the circle at points B and D.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\nscene.relate.line_extension_intersects_circle_at(line_EF, circle1, B, D)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)"}, "Rels": ["is_diameter(line_BD, circle1)", "perpendicular(line_BD, line_AC)", "line_extension_intersects_circle_at(line_EF, circle1, B, D)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [0.40957608166779425, 1.1133880178064015], "B": [0.3369761298787747, 1.3373487637728763], "C": [-1.438719546013003, 0.5142385330115345], "D": [0.48217579155991946, 0.8894272732290887], "E": [1.6348662320219711, -2.6664720320640023], "F": [1.3185234215508976, -1.690595932787008]}, "circles": {"A": 0.23543394877685597}}}
{"unique_id": "1obj_3rel_3extra_gen0019", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a right trapezoid ABCD. There is a line segment AC. There is a line segment BD. There is a line segment AD. There is a line segment DC. Line segment AC intersects line segment BD at point E. Line segment AD is perpendicular to line segment DC. Angle ADC is a right angle. Further, length of line segment AD is equal to length of line segment DC, length of line segment AC is less than or equal to twice the length of line segment AD, and angle ADC is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ntrapezoid1 = scene.add.right_trapezoid(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_AD = scene.add.line_segment(A, D)\nline_DC = scene.add.line_segment(D, C)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_BD, E)\nscene.relate.perpendicular(line_AD, line_DC)\nscene.relate.right_angle(A, D, C)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_DC.length)\nscene.constraint.leq(line_AC.length, 2 * line_AD.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "right_trapezoid(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_AD": "line_segment(A, D)", "line_DC": "line_segment(D, C)"}, "Rels": ["lines_intersect_at(line_AC, line_BD, E)", "perpendicular(line_AD, line_DC)", "right_angle(A, D, C)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_DC').length)", "scene.constraint.leq(scene.get_object('line_AC').length, 2 * scene.get_object('line_AD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [4.539379808223095, -1.2642014900247704], "B": [1.9744083882846135, -1.178441364205914], "C": [0.7496019599930323, 2.787766098591673], "D": [4.670474659595131, 2.6566712494620246], "E": [3.040627809366216, 0.33823930125884955]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0020", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is an obtuse triangle with vertices A, B, C. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment GH. H is the orthocenter of triangle ABC. Line AD is an altitude of triangle ABC from vertex A. Line BE is an altitude of triangle ABC from vertex B. Further, the length of line AD is equal to the length of line BE. Further, the area of triangle ABC is less than or equal to 20. Further, the angle at vertex A of triangle ABC is 120 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangleABC = scene.add.obtuse_triangle(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_GH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.is_orthocenter(H, triangleABC)\nscene.relate.is_altitude(line_AD, triangleABC, A)\nscene.relate.is_altitude(line_BE, triangleABC, B)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BE.length)\nscene.constraint.leq(triangleABC.area, 20)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 120)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "obtuse_triangle(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_GH": "line_segment(G, H)"}, "Rels": ["is_orthocenter(H, triangleABC)", "is_altitude(line_AD, triangleABC, A)", "is_altitude(line_BE, triangleABC, B)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)", "scene.constraint.leq(scene.get_object('triangleABC').area, 20)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 120)"], "possible_solution": {"points": {"A": [-2.155066383088679, 0.12327986295849579], "B": [-1.8817812048384959, 0.4154483289549973], "C": [7.445803873217926, -1.752971867848233], "D": [-2.0772864054861557, 0.4584183048114216], "E": [-1.947305667824633, 0.08024333971826991], "F": [0.9390146740726317, -4.3569029389222], "G": [8.277878641061964, 2.1578871257324272], "H": [-0.7985220083657829, 5.958522807499637]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0021", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is an isosceles triangle ABC with AB = BC. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment BC. Line AD is a median of triangle ABC from vertex A. Line AD is perpendicular to line BC. Point E is the orthocenter of triangle ABC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ntriangleABC = scene.add.isosceles_triangle(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_BC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.is_median(line_AD, triangleABC, A)\nscene.relate.perpendicular(line_AD, line_BC)\nscene.relate.is_orthocenter(E, triangleABC)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "isosceles_triangle(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_BC": "line_segment(B, C)"}, "Rels": ["is_median(line_AD, triangleABC, A)", "perpendicular(line_AD, line_BC)", "is_orthocenter(E, triangleABC)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.8956305261913461, 2.6635598094743296], "B": [2.5558104244187514, -0.32137724028990095], "C": [-1.7549413914050374, -1.8179442232313037], "D": [0.4004344812681543, -1.0696607402124678], "E": [-0.03158712692598337, 0.17474613533891392], "F": [-0.41545147793069337, -7.274335680212139]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0024", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There are line segments BD, AC, and EF. Line BD is a diameter of the circle. Line BD is perpendicular to line AC. Line AC and line EF intersect at point A.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\nscene.relate.lines_intersect_at(line_AC, line_EF, A)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)"}, "Rels": ["is_diameter(line_BD, circle1)", "perpendicular(line_BD, line_AC)", "lines_intersect_at(line_AC, line_EF, A)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.5485227236890091, -1.0346894954026207], "B": [-0.08458763761193233, -1.298775074255518], "C": [-1.551908383633495, -2.797397481357387], "D": [-1.0124577541375948, -0.7706038687277624], "E": [0.3348508690991603, -0.5269812939229999], "F": [-3.342038598297736, -2.640228719650537]}, "circles": {"A": 0.5338323046728065}}}
{"unique_id": "1obj_3rel_3extra_gen0030", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There is a line segment BD. There is a line segment AC. There is a line segment EF. Line BD is a diameter of the circle. Line BD is perpendicular to line AC. Angle EAF is acute. Further, the length of line AC is equal to half the length of line BD. Further, the length of line EF is less than or equal to the diameter of the circle. Further, the angle EAF measures exactly 30 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\nscene.relate.acute_angle(E, A, F)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length / 2)\nscene.constraint.leq(line_EF.length, circle1.diameter)\nscene.constraint.eq(scene.angle(scene.get_object('E'), scene.get_object('A'), scene.get_object('F')), 30)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)"}, "Rels": ["is_diameter(line_BD, circle1)", "perpendicular(line_BD, line_AC)", "acute_angle(E, A, F)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length / 2)", "scene.constraint.leq(scene.get_object('line_EF').length, scene.get_object('circle1').diameter)", "scene.constraint.eq(scene.angle(scene.get_object('E'), scene.get_object('A'), scene.get_object('F')), 30)"], "possible_solution": {"points": {"A": [1.5176638668375924, 0.1555412741067958], "B": [-0.31723287948708884, -0.9508798399103611], "C": [2.624085009283893, -1.6793555143401395], "D": [3.3525606262192396, 1.2619623912048132], "E": [-0.04515536737741682, -2.6414089041180926], "F": [1.5994347120250805, -5.66150168835827]}, "circles": {"A": 2.14266511586078}}}
{"unique_id": "1obj_3rel_3extra_gen0032", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There are line segments BD, AC, and EF. Line BD is a diameter of the circle. Line EF is a chord of the circle. Line BD intersects line AC at point A.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_BD, line_AC, A)\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.is_chord(line_EF, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)"}, "Rels": ["lines_intersect_at(line_BD, line_AC, A)", "is_diameter(line_BD, circle1)", "is_chord(line_EF, circle1)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [1.2163832529497351, 1.4482261930599567], "B": [1.3065218409211086, -0.34263915422327423], "C": [4.81289112475681, 2.392296565490159], "D": [1.1262446734370666, 3.2390915547019294], "E": [2.4291322412227543, 0.1274069092935729], "F": [0.04766427503782187, 2.8081598889741763]}, "circles": {"A": 1.793132368800803}}}
{"unique_id": "1obj_3rel_3extra_gen0033", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a trapezoid ABCD. There are line segments AC, BD, EF. The trapezoid is similar to itself. Line AC is perpendicular to line BD. Point F is the midpoint of line BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ntrapezoid1 = scene.add.trapezoid(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.similar(trapezoid1, trapezoid1)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.is_midpoint(F, line_BD)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "trapezoid(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["similar(trapezoid1, trapezoid1)", "perpendicular(line_AC, line_BD)", "is_midpoint(F, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.35017140828799126, 1.124589966629249], "B": [1.8570443253785502, -0.9497362742618927], "C": [0.5873216274726433, 1.2875603595405722], "D": [1.6401160585734502, 0.298151359621935], "E": [-5.065906471162807, 7.085073511851329], "F": [1.7485802062684235, -0.32579245373888627]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0035", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a trapezoid ABCD. There is a line segment AC. There is a line segment BD. There is a line segment AD. There is a line segment BC. The trapezoid ABCD is similar to itself. Line AC is perpendicular to line BD. Point E is the midpoint of line AD. Further, the length of line AD is equal to the length of line BC. Further, the length of line AC is less than or equal to twice the length of line AD. Further, angle ADC is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ntrapezoid1 = scene.add.trapezoid(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_AD = scene.add.line_segment(A, D)\nline_BC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.similar(trapezoid1, trapezoid1)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.is_midpoint(E, line_AD)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BC.length)\nscene.constraint.leq(line_AC.length, 2 * line_AD.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "trapezoid(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_AD": "line_segment(A, D)", "line_BC": "line_segment(B, C)"}, "Rels": ["similar(trapezoid1, trapezoid1)", "perpendicular(line_AC, line_BD)", "is_midpoint(E, line_AD)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BC').length)", "scene.constraint.leq(scene.get_object('line_AC').length, 2 * scene.get_object('line_AD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [-7.8592932027741185, -5.681808319045747], "B": [-7.852173875997065, 9.999237353382295], "C": [7.8324206549547, 9.999208822622885], "D": [7.825298132323861, -5.6889288730168595], "E": [-0.01699715899832078, -5.685368708580095]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0036", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a triangle ABC. There is a line AD. There is a line BE. There is a line CF. AD is an altitude of triangle ABC from vertex A. BE is a median of triangle ABC from vertex B. AD and BE intersect at point G. Further, the length of line AD is equal to the length of line BE, the length of line CF is less than or equal to 3 units, and angle ADB is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\nline_altitude = scene.add.line_segment(A, D)\nline_median = scene.add.line_segment(B, E)\nline_perpendicular = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude, triangleABC, A)\nscene.relate.is_median(line_median, triangleABC, B)\nscene.relate.lines_intersect_at(line_altitude, line_median, G)\n\n### Extra relationships\n\nscene.constraint.eq(line_altitude.length, line_median.length)\nscene.constraint.leq(line_perpendicular.length, 3.0)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('B')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "line_altitude": "line_segment(A, D)", "line_median": "line_segment(B, E)", "line_perpendicular": "line_segment(C, F)"}, "Rels": ["is_altitude(line_altitude, triangleABC, A)", "is_median(line_median, triangleABC, B)", "lines_intersect_at(line_altitude, line_median, G)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_altitude').length, scene.get_object('line_median').length)", "scene.constraint.leq(scene.get_object('line_perpendicular').length, 3.0)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('B')), 90)"], "possible_solution": {"points": {"A": [2.300979897433891, -2.4015492967883043], "B": [-4.006435315145543, -3.0711846915202146], "C": [-1.397578464355187, 1.987270579840223], "D": [-2.408424032522196, 0.02728701865813243], "E": [0.4517007659696176, -0.20713939611404844], "F": [-1.9796699993446185, -0.5754958492692498], "G": [-0.6195204476527107, -0.8953252449468373]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0037", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There are line segments BD, AC, and EF. Line BD is a diameter of the circle. Line BD is perpendicular to line AC. Line AC is parallel to line EF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\nscene.relate.parallel(line_AC, line_EF)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)"}, "Rels": ["is_diameter(line_BD, circle1)", "perpendicular(line_BD, line_AC)", "parallel(line_AC, line_EF)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [0.864329394681122, -4.468154147622227], "B": [0.1485845107558331, -4.718886694290422], "C": [0.36751196832388905, -3.0499316856595966], "D": [1.5800742844498286, -4.217421613145682], "E": [-6.166512784136019, 4.270007188107013], "F": [-5.291605090388457, 1.7724825993731264]}, "circles": {"A": 0.7583914280431407}}}
{"unique_id": "1obj_3rel_3extra_gen0041", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a rhomboid ABCD. There are line segments AC, BD, and BE. Line AC is perpendicular to line BD. Line BE is the bisector of angle ABD. Point E lies on line AC. Further, the length of line AC is equal to twice the length of line BD. Further, the length of line BE is less than or equal to the length of line AC. Further, the measure of angle ABD is 60 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nrhomboid1 = scene.add.rhomboid(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_angle_bisector = scene.add.line_segment(B, E)\n\n### relationships\n\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.angle_bisector(A, B, D, line_angle_bisector)\nscene.relate.point_lies_on(E, line_AC)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, 2 * line_BD.length)\nscene.constraint.leq(line_angle_bisector.length, line_AC.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('D')), 60)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rhomboid1": "rhomboid(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_angle_bisector": "line_segment(B, E)"}, "Rels": ["perpendicular(line_AC, line_BD)", "angle_bisector(A, B, D, line_angle_bisector)", "point_lies_on(E, line_AC)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, 2 * scene.get_object('line_BD').length)", "scene.constraint.leq(scene.get_object('line_angle_bisector').length, scene.get_object('line_AC').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('D')), 60)"], "possible_solution": {"points": {"A": [0.7381139955055463, -0.35173836509466655], "B": [0.4194180374330696, -0.1594158267639828], "C": [0.06904148545534632, -0.3128852792794036], "D": [0.41291058386386476, -0.4953695289415054], "E": [0.5171688777031843, -0.3365616953067731]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0042", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a triangle with points A, B, C. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is an altitude of triangle ABC from vertex A. Line BE is a median of triangle ABC from vertex B. Line AD and line BE intersect at point G.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\nline_altitude = scene.add.line_segment(A, D)\nline_median = scene.add.line_segment(B, E)\nline_perpendicular = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude, triangleABC, A)\nscene.relate.is_median(line_median, triangleABC, B)\nscene.relate.lines_intersect_at(line_altitude, line_median, G)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "line_altitude": "line_segment(A, D)", "line_median": "line_segment(B, E)", "line_perpendicular": "line_segment(C, F)"}, "Rels": ["is_altitude(line_altitude, triangleABC, A)", "is_median(line_median, triangleABC, B)", "lines_intersect_at(line_altitude, line_median, G)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [1.1637009936995342, 1.1920933494121615], "B": [-0.4260121408231572, -0.7276755110631319], "C": [8.909436648750725, -3.615413231813691], "D": [0.4828897849728479, -1.0088263998292997], "E": [5.036568921553338, -1.2116599117390623], "F": [-4.800372657860155, 4.012875457728343], "G": [0.5432928821629146, -0.8135558754037205]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0048", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There are line segments BD, AC, and EF. Line BD is a diameter of the circle. Line BD is perpendicular to line AC. Points E, F, and A are collinear.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\nscene.relate.collinear(E, F, A)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)"}, "Rels": ["is_diameter(line_BD, circle1)", "perpendicular(line_BD, line_AC)", "collinear(E, F, A)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.7324695742279873, 3.258302344200161], "B": [-2.0828230611470295, 4.858905039868127], "C": [0.06719295188979961, 3.9329401706989318], "D": [0.617883940795392, 1.6576996871302458], "E": [2.1947042342042042, -2.8452075681627638], "F": [1.0879173448912294, -0.5374236010756918]}, "circles": {"A": 2.094130726806795}}}
{"unique_id": "1obj_3rel_3extra_gen0052", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a major arc with center A, start point B, and end point C. There is a line segment AD. There is a line segment BE. There is a line segment CD. Line AD is perpendicular to line BE. Point D lies on the major arc. Point E is the midpoint of line CD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nsemicircle1 = scene.add.major_arc(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CD = scene.add.line_segment(C, D)\n\n### relationships\n\nscene.relate.perpendicular(line_AD, line_BE)\nscene.relate.point_lies_on(D, semicircle1)\nscene.relate.is_midpoint(E, line_CD)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"semicircle1": "major_arc(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CD": "line_segment(C, D)"}, "Rels": ["perpendicular(line_AD, line_BE)", "point_lies_on(D, semicircle1)", "is_midpoint(E, line_CD)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [1.2820531673750362, -3.420347576362234], "B": [0.16160448700248356, -4.052494913354546], "C": [1.1538915086490094, -2.1402733219995267], "D": [0.050570162919439984, -3.0482385658205646], "E": [0.6022308341528952, -2.594255935250146]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0054", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a triangle ABC. There is a line segment AD. There is a line segment BE. There is a line segment FG. Line AD is an altitude of triangle ABC from vertex A. Line BE is a median of triangle ABC from vertex B. Point H is the orthocenter of triangle ABC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\nline_altitude = scene.add.line_segment(A, D)\nline_median = scene.add.line_segment(B, E)\nline_perp_bisector = scene.add.line_segment(F, G)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude, triangleABC, A)\nscene.relate.is_median(line_median, triangleABC, B)\nscene.relate.is_orthocenter(H, triangleABC)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "line_altitude": "line_segment(A, D)", "line_median": "line_segment(B, E)", "line_perp_bisector": "line_segment(F, G)"}, "Rels": ["is_altitude(line_altitude, triangleABC, A)", "is_median(line_median, triangleABC, B)", "is_orthocenter(H, triangleABC)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [-6.336712971936232, -7.473413778146593], "B": [3.8830203770293164, -5.547287809583887], "C": [-4.251948684310554, 6.586541881959494], "D": [1.6047785708353755, -2.1491435963730114], "E": [-5.294330794654959, -0.44343599990273014], "F": [-6.426768095335104, 6.079294283814714], "G": [1.6945265226495063, -0.22746751147706767], "H": [-2.13319929024409, -4.655222443550671]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0055", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There is a line segment BD. There is a line segment AC. There is a line segment EF. Line BD is a diameter of the circle. Line BD is perpendicular to line AC. Line BD is congruent to line EF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\nscene.relate.congruent(line_BD, line_EF)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)"}, "Rels": ["is_diameter(line_BD, circle1)", "perpendicular(line_BD, line_AC)", "congruent(line_BD, line_EF)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-1.8539636311579788, 2.1508662307447763], "B": [-1.5688692728430513, 2.5154866872506187], "C": [-2.8004176398750316, 2.8908924663880398], "D": [-2.139057968734973, 1.7862458043698186], "E": [-0.44283171197085663, 5.897123118526158], "F": [-0.2651252705826032, 4.988647573672948]}, "circles": {"A": 0.46284648183904986}}}
{"unique_id": "1obj_3rel_3extra_gen0057", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is an acute triangle with vertices A, B, C. There is a line segment AD. There is a line segment BE. There is a line segment FG. AD is an altitude of triangle ABC from vertex A. BE is a median of triangle ABC from vertex B. AD is perpendicular to BE.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntriangleABC = scene.add.acute_triangle(A, B, C)\nline_altitude = scene.add.line_segment(A, D)\nline_median = scene.add.line_segment(B, E)\nline_perp_bisector = scene.add.line_segment(F, G)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude, triangleABC, A)\nscene.relate.is_median(line_median, triangleABC, B)\nscene.relate.perpendicular(line_altitude, line_median)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "acute_triangle(A, B, C)", "line_altitude": "line_segment(A, D)", "line_median": "line_segment(B, E)", "line_perp_bisector": "line_segment(F, G)"}, "Rels": ["is_altitude(line_altitude, triangleABC, A)", "is_median(line_median, triangleABC, B)", "perpendicular(line_altitude, line_median)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [-3.625690225588972, -0.745255530762407], "B": [9.354255788054138, 8.234075539064209], "C": [-7.231955761264025, -3.553535123971167], "D": [-3.5107317071861703, -0.9089196298603327], "E": [-5.428823474168313, -2.149400615996589], "F": [-0.06937735653126298, -6.714992116099262], "G": [-8.066334140326218, -1.4325523472028863]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0060", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is an obtuse triangle ABC. There is a line segment AD. There is a line segment EF. There is a line segment BC. There is a line BC. There is a line DE. Line AD is an altitude of triangle ABC from vertex A. Line EF is the perpendicular bisector of line BC. Lines BC and DE intersect at point G.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntriangleABC = scene.add.obtuse_triangle(A, B, C)\nline_altitude_from_A = scene.add.line_segment(A, D)\nline_perpendicular_bisector = scene.add.line_segment(E, F)\nline_BC = scene.add.line_segment(B, C)\nline_extension1 = scene.add.line(B, C)\nline_extension2 = scene.add.line(D, E)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude_from_A, triangleABC, A)\nscene.relate.perpendicular_bisector_at(line_BC, line_perpendicular_bisector)\nscene.relate.line_extensions_intersect_at(line_extension1, line_extension2, G)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "obtuse_triangle(A, B, C)", "line_altitude_from_A": "line_segment(A, D)", "line_perpendicular_bisector": "line_segment(E, F)", "line_BC": "line_segment(B, C)", "line_extension1": "line(B, C)", "line_extension2": "line(D, E)"}, "Rels": ["is_altitude(line_altitude_from_A, triangleABC, A)", "perpendicular_bisector_at(line_BC, line_perpendicular_bisector)", "line_extensions_intersect_at(line_extension1, line_extension2, G)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [-8.038932623063259, 3.8732367309886166], "B": [6.921992491927424, -5.879472549188002], "C": [-6.184425173161594, 6.7660312198694434], "D": [-5.700368037422764, 6.297142284459582], "E": [6.542336296032313, -5.6521160279018705], "F": [6.681195921997434, -5.508195333002777], "G": [-5.866993848191512, 6.459768663292244]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0061", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There is a line segment BD. There is a line segment AC. There is a line segment EF. Line BD is a diameter of the circle. Line BD is perpendicular to line AC. Line AC and line EF intersect at point A. Further, the area of the circle is 16π. Further, the length of line EF is less than or equal to the length of line AC. Further, angle BAE is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\nscene.relate.lines_intersect_at(line_AC, line_EF, A)\n\n### Extra relationships\n\nscene.constraint.eq(circle1.area, 16 * 3.14159)\nscene.constraint.leq(line_EF.length, line_AC.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('E')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)"}, "Rels": ["is_diameter(line_BD, circle1)", "perpendicular(line_BD, line_AC)", "lines_intersect_at(line_AC, line_EF, A)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('circle1').area, 16 * 3.14159)", "scene.constraint.leq(scene.get_object('line_EF').length, scene.get_object('line_AC').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('E')), 90)"], "possible_solution": {"points": {"A": [-0.6193202573622951, 2.180222411882138], "B": [1.1644568208231627, 5.760463410984763], "C": [5.0674491548666225, -0.6530865378196546], "D": [-2.4030973311010406, -1.4000185750584304], "E": [2.734892216132928, 0.5090591297498278], "F": [-1.2922252993511076, 2.5154828092477794]}, "circles": {"A": 3.999998301523332}}}
{"unique_id": "1obj_3rel_3extra_gen0063", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a rectangle with A, B, C, D. There is a line segment AC. There is a line segment BD. There is a line segment DE. The line segment DE is the angle bisector of angle ADC. The line segments AC and BD are perpendicular. Point E is the midpoint of line segment AC. Further, the length of line AC is equal to the length of line BD. Further, the area of the rectangle is at most 20. Further, angle ADC is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_angle_bisector = scene.add.line_segment(D, E)\n\n### relationships\n\nscene.relate.angle_bisector(A, D, C, line_angle_bisector)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.is_midpoint(E, line_AC)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.leq(rectangle1.area, 20)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_angle_bisector": "line_segment(D, E)"}, "Rels": ["angle_bisector(A, D, C, line_angle_bisector)", "perpendicular(line_AC, line_BD)", "is_midpoint(E, line_AC)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.leq(scene.get_object('rectangle1').area, 20)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [2.8535550897128337, 1.4584072252737854], "B": [-1.3259006079690674, 1.6718554080949084], "C": [-1.5393487899197145, -2.507600318590704], "D": [2.640106901170091, -2.721048504161043], "E": [0.6571029319428577, -0.5245963291315215]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0066", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a major arc with center A and endpoints B and C. There is a line segment DE. There is a line segment CF. There is a line segment GH. Line DE and line CF intersect at point G, and their extensions meet at G. Point D lies on the major arc. Point F lies on the major arc. Further, the length of line DE is equal to the length of line CF. Further, the inscribed angle of the major arc is less than or equal to 90 degrees. Further, the angle DAF is 60 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\nmajor_arc1 = scene.add.major_arc(A, B, C)\nline_DE = scene.add.line_segment(D, E)\nline_CF = scene.add.line_segment(C, F)\nline_GH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line_DE, line_CF, G)\nscene.relate.point_lies_on(D, major_arc1)\nscene.relate.point_lies_on(F, major_arc1)\n\n### Extra relationships\n\nscene.constraint.eq(line_DE.length, line_CF.length)\nscene.constraint.leq(major_arc1.inscribed_angle, 90)\nscene.constraint.eq(scene.angle(scene.get_object('D'), scene.get_object('A'), scene.get_object('F')), 60)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"major_arc1": "major_arc(A, B, C)", "line_DE": "line_segment(D, E)", "line_CF": "line_segment(C, F)", "line_GH": "line_segment(G, H)"}, "Rels": ["line_extensions_intersect_at(line_DE, line_CF, G)", "point_lies_on(D, major_arc1)", "point_lies_on(F, major_arc1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_DE').length, scene.get_object('line_CF').length)", "scene.constraint.leq(scene.get_object('major_arc1').inscribed_angle, 90)", "scene.constraint.eq(scene.angle(scene.get_object('D'), scene.get_object('A'), scene.get_object('F')), 60)"], "possible_solution": {"points": {"A": [-1.1333477148533615, 2.383212869643357], "B": [-3.1121596210252314, 3.467115047655255], "C": [0.8323498378581545, 1.275368614938813], "D": [1.0531212297300958, 2.94025202200515], "E": [-0.8238064527593992, -0.07028940963956216], "F": [-0.5225069265426177, 4.5553004783316995], "G": [0.5065720884311963, 2.0635000183655707], "H": [7.986158156968865, -2.353761743591151]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0069", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a right trapezoid ABCD. There is a line segment AC. There is a line segment BD. There is a line segment AD. There is a line segment BC. There is a line segment AB. Line AB is rotated 90 degrees counterclockwise around point A to align with line AD. Line AC is perpendicular to line BD. Point E is the midpoint of line AC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ntrapezoid1 = scene.add.right_trapezoid(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_AD = scene.add.line_segment(A, D)\nline_BC = scene.add.line_segment(B, C)\nline_AB = scene.add.line_segment(A, B)\n\n### relationships\n\nscene.relate.rotation_around_point(line_AB, line_AD, A, 90)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.is_midpoint(E, line_AC)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "right_trapezoid(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_AD": "line_segment(A, D)", "line_BC": "line_segment(B, C)", "line_AB": "line_segment(A, B)"}, "Rels": ["rotation_around_point(line_AB, line_AD, A, 90)", "perpendicular(line_AC, line_BD)", "is_midpoint(E, line_AC)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [-2.7437361273901195, 2.1924975115288934], "B": [-2.9591196020481676, 2.590938641460193], "C": [-2.560678478659987, 2.806321980214481], "D": [-2.34529505384045, 2.4078810176334913], "E": [-2.6522073094226726, 2.49940971917443]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0073", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a circle with center A. There are line segments BD, AC, and ED. Line BD is a diameter of the circle. Line BD is perpendicular to line AC. Angle EDB is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_ED = scene.add.line_segment(E, D)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\nscene.relate.right_angle(E, D, B)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_ED": "line_segment(E, D)"}, "Rels": ["is_diameter(line_BD, circle1)", "perpendicular(line_BD, line_AC)", "right_angle(E, D, B)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [-3.311892231229627, -3.2252300258361433], "B": [-2.8257786090843644, -4.616801974679952], "C": [-0.552932065690859, -2.26145078579732], "D": [-3.7980058555974106, -1.833658117991553], "E": [-2.8201210451635896, -1.4920565518353253]}, "circles": {"A": 1.4740348974909603}}}
{"unique_id": "1obj_3rel_3extra_gen0076", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There is a line segment BD. There is a line segment AC. There is a line segment EF. Line BD is a diameter of the circle. Line BD is perpendicular to line AC. Line BD is congruent to line EF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\nscene.relate.congruent(line_BD, line_EF)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)"}, "Rels": ["is_diameter(line_BD, circle1)", "perpendicular(line_BD, line_AC)", "congruent(line_BD, line_EF)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.09837722704515858, 1.1415161997841325], "B": [-0.9025045278055293, 0.9388405558263709], "C": [-0.4861634299731917, 2.6800802670516886], "D": [0.7057500913411302, 1.3441918591181437], "E": [1.5949081182556877, 6.2704600401501285], "F": [3.015154892395485, 7.127018164439799]}, "circles": {"A": 0.8292756844139538}}}
{"unique_id": "1obj_3rel_3extra_gen0078", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a triangle ABC. There is a line AD. There is a line BE. There is a line CF. There is a line GH. Angle ABC is acute. Line AD is an altitude of triangle ABC from vertex A. Line BE is the mirror image of line CF across line GH. Further, the circumradius of triangle ABC is 2.0, the length of line BE is less than or equal to the length of line CF, and angle ABC is 60 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangle_ABC = scene.add.equilateral_triangle(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_GH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.acute_angle(A, B, C)\nscene.relate.is_altitude(line_AD, triangle_ABC, A)\nscene.relate.mirror_across_line(line_BE, line_CF, line_GH)\n\n### Extra relationships\n\nscene.constraint.eq(triangle_ABC.circumradius, 2.0)\nscene.constraint.leq(line_BE.length, line_CF.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 60)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle_ABC": "equilateral_triangle(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_GH": "line_segment(G, H)"}, "Rels": ["acute_angle(A, B, C)", "is_altitude(line_AD, triangle_ABC, A)", "mirror_across_line(line_BE, line_CF, line_GH)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle_ABC').circumradius, 2.0)", "scene.constraint.leq(scene.get_object('line_BE').length, scene.get_object('line_CF').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 60)"], "possible_solution": {"points": {"A": [-3.386198043716122, -0.4206179059675913], "B": [0.029867982729638656, -0.9955034045725506], "C": [-1.1803000509154862, 2.250340509687164], "D": [-0.5752171824430067, 0.6274176228052774], "E": [-0.9523579938338149, 8.770421190030044], "F": [4.47066550686515, -5.77491316296819], "G": [-6.939531226111453, -1.7454281418938993], "H": [9.757616082707685, 4.47986924661877]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0082", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There is a line segment BD. There is a line segment AC. There is a line segment EF. Line BD is a diameter of the circle. Line BD is perpendicular to line AC. Point E lies on the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\nscene.relate.point_lies_on(E, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)"}, "Rels": ["is_diameter(line_BD, circle1)", "perpendicular(line_BD, line_AC)", "point_lies_on(E, circle1)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [0.4985103580809264, 0.19956848679849196], "B": [0.3432816619416757, 0.34659329847557413], "C": [2.117589565497806, 1.9089898821900757], "D": [0.6537388194540593, 0.052543634703695066], "E": [0.7059851335752899, 0.25120709964302196], "F": [3.946785387321023, -4.726754928578702]}, "circles": {"A": 0.21380435353651492}}}
{"unique_id": "1obj_3rel_3extra_gen0084", "nl_description": "Diagram description: The diagram contains points A, B, C, D, M, N. There is an isosceles trapezoid ABCD. There is a line segment AC. There is a line segment BD. There is a line segment MN. M is the midpoint of line AC. line AC is perpendicular to line BD. line MN is parallel to line AC. Further, length of line AC is equal to length of line BD, area of trapezoid ABCD is less than or equal to 20, and angle AMB is equal to 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, M, N = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"M\", \"N\"])\n\ntrapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_MN = scene.add.line_segment(M, N)\n\n### relationships\n\nscene.relate.is_midpoint(M, line_AC)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.parallel(line_MN, line_AC)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.leq(trapezoid1.area, 20)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('M'), scene.get_object('B')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "isosceles_trapezoid(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_MN": "line_segment(M, N)"}, "Rels": ["is_midpoint(M, line_AC)", "perpendicular(line_AC, line_BD)", "parallel(line_MN, line_AC)"], "Points": ["A", "B", "C", "D", "M", "N"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.leq(scene.get_object('trapezoid1').area, 20)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('M'), scene.get_object('B')), 90)"], "possible_solution": {"points": {"A": [0.5159749033617645, 1.158526973519104], "B": [2.714358605461745, 0.17370482418228894], "C": [1.7295357172642443, -2.0246763619786545], "D": [-0.4688446826743129, -1.039855466887573], "M": [1.1227559480164544, -0.43307607669751175], "N": [0.42767629677812485, 1.390137555976517]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0087", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a major arc with center A from B to C. There are line segments DE, CF, and AG. The extensions of line DE and line CF intersect at point G. Point D lies on the major arc with center A from B to C. Point F lies on the major arc with center A from B to C. Further, length of line AG is equal to length of line DE. Further, length of line CF is less than or equal to the length of line AG. Further, angle DGF is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\narc1 = scene.add.major_arc(A, B, C)\nline_DE = scene.add.line_segment(D, E)\nline_CF = scene.add.line_segment(C, F)\nline_AG = scene.add.line_segment(A, G)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line_DE, line_CF, G)\nscene.relate.point_lies_on(D, arc1)\nscene.relate.point_lies_on(F, arc1)\n\n### Extra relationships\n\nscene.constraint.eq(line_AG.length, line_DE.length)\nscene.constraint.leq(line_CF.length, line_AG.length)\nscene.constraint.eq(scene.angle(scene.get_object('D'), scene.get_object('G'), scene.get_object('F')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"arc1": "major_arc(A, B, C)", "line_DE": "line_segment(D, E)", "line_CF": "line_segment(C, F)", "line_AG": "line_segment(A, G)"}, "Rels": ["line_extensions_intersect_at(line_DE, line_CF, G)", "point_lies_on(D, arc1)", "point_lies_on(F, arc1)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AG').length, scene.get_object('line_DE').length)", "scene.constraint.leq(scene.get_object('line_CF').length, scene.get_object('line_AG').length)", "scene.constraint.eq(scene.angle(scene.get_object('D'), scene.get_object('G'), scene.get_object('F')), 90)"], "possible_solution": {"points": {"A": [-1.235563008023023, 0.8697489578957041], "B": [-3.4264470597981136, 2.169362409673116], "C": [1.1420249340853028, -0.044603962042937685], "D": [-2.6398230016729376, 2.995078380564408], "E": [0.32486057246363254, 2.248393400651286], "F": [1.29148516700282, 0.5488220975093904], "G": [1.6363469831751054, 1.9180832825698013]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0093", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There are line segments BD, AC, and EF. Line BD is a diameter of the circle. Point B lies on the circle. Line BD is perpendicular to line AC. Further, length of line AC is equal to half the length of line BD. Further, length of line EF is less than or equal to length of line AC. Further, angle BAC is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.point_lies_on(B, circle1)\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length / 2)\nscene.constraint.leq(line_EF.length, line_AC.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)"}, "Rels": ["point_lies_on(B, circle1)", "is_diameter(line_BD, circle1)", "perpendicular(line_BD, line_AC)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length / 2)", "scene.constraint.leq(scene.get_object('line_EF').length, scene.get_object('line_AC').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [-1.052090623183553, 2.051403209678366], "B": [1.0269351172505676, -1.3027295947193511], "C": [-4.406223472117703, -0.027622558374057297], "D": [-3.1311163598800857, 5.405536016311219], "E": [0.05369752058343047, -4.1076257251590516], "F": [1.9981309932412594, -2.245226803966272]}, "circles": {"A": 3.9462076535665465}}}
{"unique_id": "1obj_3rel_3extra_gen0096", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a major arc with center A and endpoints B and C. There is a line segment DE. There is a line segment CF. There is a line segment GH. Point D lies on the major arc with center A and endpoints B and C. Point F lies on the major arc with center A and endpoints B and C. The extensions of line DE and line CF intersect at point G.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\nmajor_arc1 = scene.add.major_arc(A, B, C)\nline_DE = scene.add.line_segment(D, E)\nline_CF = scene.add.line_segment(C, F)\nline_GH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line_DE, line_CF, G)\nscene.relate.point_lies_on(D, major_arc1)\nscene.relate.point_lies_on(F, major_arc1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"major_arc1": "major_arc(A, B, C)", "line_DE": "line_segment(D, E)", "line_CF": "line_segment(C, F)", "line_GH": "line_segment(G, H)"}, "Rels": ["line_extensions_intersect_at(line_DE, line_CF, G)", "point_lies_on(D, major_arc1)", "point_lies_on(F, major_arc1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [1.185302901661984, -0.5724215782221053], "B": [2.0206091373458976, -0.5818584169607917], "C": [1.2464858683656403, -1.4055375432753492], "D": [1.4656062916908508, -1.3593495015249148], "E": [6.7062190091198515, 3.64482046173141], "F": [1.993321476908416, -0.7843922821943307], "G": [2.570130214152658, -0.3046588117692474], "H": [-10.0, -2.7580783519283543]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0097", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a triangle with vertices A, B, C. There is a line segment AD. There is a line segment EF. There is a line segment BG. Line AD is an altitude of triangle ABC from vertex A. Point H is the orthocenter of triangle ABC. Line BG is a median of triangle ABC from vertex B.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\nline_altitude_from_A = scene.add.line_segment(A, D)\nline_perpendicular_bisector = scene.add.line_segment(E, F)\nline_median_from_B = scene.add.line_segment(B, G)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude_from_A, triangleABC, A)\nscene.relate.is_orthocenter(H, triangleABC)\nscene.relate.is_median(line_median_from_B, triangleABC, B)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "line_altitude_from_A": "line_segment(A, D)", "line_perpendicular_bisector": "line_segment(E, F)", "line_median_from_B": "line_segment(B, G)"}, "Rels": ["is_altitude(line_altitude_from_A, triangleABC, A)", "is_orthocenter(H, triangleABC)", "is_median(line_median_from_B, triangleABC, B)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [-4.669272097924529, 7.358799989912961], "B": [9.093063777811455, 6.581850041292136], "C": [-1.5426110169392893, -9.804418463272805], "D": [5.368603419086874, 0.843614417920865], "E": [-2.2864825958751003, -2.5710947829549733], "F": [7.62649636486879, 5.667747515913293], "G": [-3.105941590815826, -1.2228092322032322], "H": [-0.7184337774850134, 4.794468083090551]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0100", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There are line segments BD, AC, EF. line BD is a chord of the circle. line BD is perpendicular to line AC. point E lies on the circle. Further, the area of the circle is 16π. Further, the length of line BD is less than or equal to the length of line AC. Further, angle BAC is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_chord(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\nscene.relate.point_lies_on(E, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(circle1.area, 16 * 3.14159)\nscene.constraint.leq(line_BD.length, line_AC.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)"}, "Rels": ["is_chord(line_BD, circle1)", "perpendicular(line_BD, line_AC)", "point_lies_on(E, circle1)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('circle1').area, 16 * 3.14159)", "scene.constraint.leq(scene.get_object('line_BD').length, scene.get_object('line_AC').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [0.3980049942929839, -0.9815660180119283], "B": [3.523717958064251, -3.477543777074311], "C": [-5.2278824203227, -8.02686487763892], "D": [-2.7277079683458725, 1.514411733691377], "E": [0.8891619746016876, 2.9881633491801773], "F": [-6.834815363962152, -9.454937792061314]}, "circles": {"A": 3.999998307034492}}}
{"unique_id": "1obj_3rel_3extra_gen0102", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is an isosceles triangle ABC with vertices A, B, C. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment GH. H is the orthocenter of triangle ABC. AD is an altitude of triangle ABC from vertex A. Line BE is perpendicular to line CF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangleABC = scene.add.isosceles_triangle(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_GH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.is_orthocenter(H, triangleABC)\nscene.relate.is_altitude(line_AD, triangleABC, A)\nscene.relate.perpendicular(line_BE, line_CF)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "isosceles_triangle(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_GH": "line_segment(G, H)"}, "Rels": ["is_orthocenter(H, triangleABC)", "is_altitude(line_AD, triangleABC, A)", "perpendicular(line_BE, line_CF)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [3.082377365260561, 2.0759362614707997], "B": [2.186210308889416, -0.5191209727337396], "C": [1.3991122809973218, 2.111071835233471], "D": [1.5471148711386338, 1.6165014852640416], "E": [0.9349647700671418, 1.20641760154772], "F": [-1.3578512424868936, 0.11190569103110548], "G": [-4.408233511476498, 9.367862570295507], "H": [2.2350854850200177, 1.8223800621528072]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0103", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a minor arc BC with center A. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is perpendicular to line BE. Point D lies on arc BC. Point E is the midpoint of line AD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\narc1 = scene.add.minor_arc(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.perpendicular(line_AD, line_BE)\nscene.relate.point_lies_on(D, arc1)\nscene.relate.is_midpoint(E, line_AD)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"arc1": "minor_arc(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["perpendicular(line_AD, line_BE)", "point_lies_on(D, arc1)", "is_midpoint(E, line_AD)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [3.323629032869668, -1.863516421791465], "B": [3.710414187858519, -1.7514263131331431], "C": [2.927328794711664, -1.935022172364465], "D": [3.4199488423712405, -1.4725056423500134], "E": [3.371788972255075, -1.6680109644001013], "F": [-3.7871230674217524, 9.014687559797203]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0104", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, H. There is an obtuse triangle ABC. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is an altitude of triangle ABC from vertex A. Line BE is an altitude of triangle ABC from vertex B. Point H is the orthocenter of triangle ABC. Further, length of line AD is equal to length of line BE, area of triangle ABC is at most 20, and angle ABC is 120 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"H\"])\n\ntriangleABC = scene.add.obtuse_triangle(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_altitude(line_AD, triangleABC, A)\nscene.relate.is_altitude(line_BE, triangleABC, B)\nscene.relate.is_orthocenter(H, triangleABC)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BE.length)\nscene.constraint.leq(triangleABC.area, 20.0)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 120)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "obtuse_triangle(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["is_altitude(line_AD, triangleABC, A)", "is_altitude(line_BE, triangleABC, B)", "is_orthocenter(H, triangleABC)"], "Points": ["A", "B", "C", "D", "E", "F", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)", "scene.constraint.leq(scene.get_object('triangleABC').area, 20.0)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 120)"], "possible_solution": {"points": {"A": [-3.2146340439989523, 1.4398415346054059], "B": [-2.814209078708032, 1.4321778935711469], "C": [2.7006923866596586, -8.556595490069045], "D": [-2.91281134456465, 1.6064920461123486], "E": [-3.1094098619577957, 1.2580281452728774], "F": [-4.070538817823973, 7.226572278438908], "H": [2.957193894844671, 4.847176961764583]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0106", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is an isosceles trapezoid ABCD. There is a line segment AC. There is a line segment BD. There is a line segment AD. There is a line segment BC. Angle ADC is obtuse. Line AC is perpendicular to line BD. Point E is the midpoint of line AC. Further, the length of line AC equals the length of line BD. Further, the area of the trapezoid is at most 20. Further, angle ADC measures 120 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ntrapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_AD = scene.add.line_segment(A, D)\nline_BC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.obtuse_angle(A, D, C)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.is_midpoint(E, line_AC)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.leq(trapezoid1.area, 20.0)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('C')), 120)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "isosceles_trapezoid(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_AD": "line_segment(A, D)", "line_BC": "line_segment(B, C)"}, "Rels": ["obtuse_angle(A, D, C)", "perpendicular(line_AC, line_BD)", "is_midpoint(E, line_AC)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.leq(scene.get_object('trapezoid1').area, 20.0)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('C')), 120)"], "possible_solution": {"points": {"A": [0.8087009567581234, 3.6143224196746924], "B": [-2.1566138237116355, -1.7799608575242916], "C": [2.3486052264186332, -1.685451189219442], "D": [3.143159225698657, -0.24005669876936675], "E": [1.5786542811080824, 0.9644359854941652]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0108", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a major arc with center A and endpoints B and C. There is a line segment DE. There is a line segment CF. There is a line segment GH. Line DE intersects line CF at point C. Point D lies on the major arc. Line DE is perpendicular to line GH.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\nmajor_arc1 = scene.add.major_arc(A, B, C)\nline_DE = scene.add.line_segment(D, E)\nline_CF = scene.add.line_segment(C, F)\nline_GH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_DE, line_CF, C)\nscene.relate.point_lies_on(D, major_arc1)\nscene.relate.perpendicular(line_DE, line_GH)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"major_arc1": "major_arc(A, B, C)", "line_DE": "line_segment(D, E)", "line_CF": "line_segment(C, F)", "line_GH": "line_segment(G, H)"}, "Rels": ["lines_intersect_at(line_DE, line_CF, C)", "point_lies_on(D, major_arc1)", "perpendicular(line_DE, line_GH)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [1.0384452185150457, 0.5165376220340389], "B": [0.7681832480239723, 0.7324828345764292], "C": [1.2502064384262976, 0.24298492326183332], "D": [1.366678172146361, 0.40728116845895024], "E": [0.42616632827726375, -0.9194146665834774], "F": [-4.694679394152897, 0.31012587253150803], "G": [1.0047924201037457, 1.1887999373069162], "H": [-2.6585830013628162, 3.785814176715459]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0110", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a triangle with vertices A, B, C. There is a line segment AD. There is a line segment BE. There is a line segment AC. Line AD is an altitude of triangle ABC from vertex A. Line BE is a median of triangle ABC from vertex B. Point E lies on line AC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\nline_altitude = scene.add.line_segment(A, D)\nline_median = scene.add.line_segment(B, E)\nline_AC = scene.add.line_segment(A, C)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude, triangleABC, A)\nscene.relate.is_median(line_median, triangleABC, B)\nscene.relate.point_lies_on(E, line_AC)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "line_altitude": "line_segment(A, D)", "line_median": "line_segment(B, E)", "line_AC": "line_segment(A, C)"}, "Rels": ["is_altitude(line_altitude, triangleABC, A)", "is_median(line_median, triangleABC, B)", "point_lies_on(E, line_AC)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [0.9809562906571703, -2.8970794437089316], "B": [10.0, 7.830064948852839], "C": [1.171167818479817, -2.368942584944779], "D": [0.8283443205050705, -2.7649699776650385], "E": [1.0760620520328588, -2.6330110203113555]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0113", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is an acute triangle ABC. There is a line segment AD. There is a line segment EF. There is a line segment BG. There is a line segment BC. The line AD is an altitude of triangle ABC from vertex A. The line EF is the perpendicular bisector of line BC. Points A, D, and E are collinear. Further, the length of line AD equals the length of line BG. Further, the area of triangle ABC is at most 12. Further, the angle BAC measures 60 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntriangleABC = scene.add.acute_triangle(A, B, C)\nline_altitude_from_A = scene.add.line_segment(A, D)\nline_perpendicular_bisector = scene.add.line_segment(E, F)\nline_median_from_B = scene.add.line_segment(B, G)\nline_BC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude_from_A, triangleABC, A)\nscene.relate.perpendicular_bisector_at(line_BC, line_perpendicular_bisector)\nscene.relate.collinear(A, D, E)\n\n### Extra relationships\n\nscene.constraint.eq(line_altitude_from_A.length, line_median_from_B.length)\nscene.constraint.leq(triangleABC.area, 12.0)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 60)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "acute_triangle(A, B, C)", "line_altitude_from_A": "line_segment(A, D)", "line_perpendicular_bisector": "line_segment(E, F)", "line_median_from_B": "line_segment(B, G)", "line_BC": "line_segment(B, C)"}, "Rels": ["is_altitude(line_altitude_from_A, triangleABC, A)", "perpendicular_bisector_at(line_BC, line_perpendicular_bisector)", "collinear(A, D, E)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_altitude_from_A').length, scene.get_object('line_median_from_B').length)", "scene.constraint.leq(scene.get_object('triangleABC').area, 12.0)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 60)"], "possible_solution": {"points": {"A": [-1.9288336360264953, -2.4018421401574397], "B": [3.22810645800749, -1.5871358371230109], "C": [-0.35080991321086064, 1.7042369805859956], "D": [0.8401080967318341, 0.6090019306792338], "E": [1.3118188314951633, 1.1219225894273852], "F": [0.36839726046361326, 0.09608108924445245], "G": [4.383575155453193, 2.3367796400599263]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0115", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a trapezoid ABCD. There are line segments AC, BD, and CE. Line CE bisects the angle ACB. Line AC and line BD intersect at point F. Line CE is perpendicular to line AC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ntrapezoid1 = scene.add.trapezoid(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_angle_bisector = scene.add.line_segment(C, E)\n\n### relationships\n\nscene.relate.angle_bisector(A, C, B, line_angle_bisector)\nscene.relate.lines_intersect_at(line_AC, line_BD, F)\nscene.relate.perpendicular(line_angle_bisector, line_AC)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "trapezoid(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_angle_bisector": "line_segment(C, E)"}, "Rels": ["angle_bisector(A, C, B, line_angle_bisector)", "lines_intersect_at(line_AC, line_BD, F)", "perpendicular(line_angle_bisector, line_AC)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [2.8754515309484416, 6.96237454339336], "B": [2.8063638970812135, 6.699941907485002], "C": [-0.25608072395910403, -4.965666831213428], "D": [1.7978014137294032, 2.8327717813865902], "E": [2.6726534696959274, -5.734562758331679], "F": [2.7532233570689124, 6.496745772864235]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0116", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There is a line segment BD. There is a line segment AC. There is a line segment EF. Line BD is a diameter of the circle. Line BD is perpendicular to line AC. Line AC is parallel to line EF. Further, the length of line AC is equal to half the length of line BD. Further, the length of line EF is less than or equal to the length of line AC. Further, angle BAC is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\nscene.relate.parallel(line_AC, line_EF)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length / 2)\nscene.constraint.leq(line_EF.length, line_AC.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)"}, "Rels": ["is_diameter(line_BD, circle1)", "perpendicular(line_BD, line_AC)", "parallel(line_AC, line_EF)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length / 2)", "scene.constraint.leq(scene.get_object('line_EF').length, scene.get_object('line_AC').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [0.4216390316885132, 0.5037472697601488], "B": [2.37165087697018, 3.3938050469568974], "C": [-2.468418978315088, 2.453759269931152], "D": [-1.528372807248555, -2.3863104674099773], "E": [-4.964312610378851, -4.04676620123889], "F": [-5.346822772720384, -3.7886748535598413]}, "circles": {"A": 3.486399301680719}}}
{"unique_id": "1obj_3rel_3extra_gen0117", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There are line segments BD, AC, and EF. Line BD is a diameter of the circle. Line BD is perpendicular to line AC. Points E, F, and A are collinear.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\nscene.relate.collinear(E, F, A)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)"}, "Rels": ["is_diameter(line_BD, circle1)", "perpendicular(line_BD, line_AC)", "collinear(E, F, A)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [1.6860729319548227, 2.0932061392165533], "B": [1.8783146166311477, 2.2578069276004746], "C": [2.1236976758854715, 1.5820922327196165], "D": [1.4938312099674436, 1.9286054803465538], "E": [-0.5574478702236363, 2.5543767519483973], "F": [0.6821280875228012, 2.2995736766579453]}, "circles": {"A": 0.2530815528073547}}}
{"unique_id": "1obj_3rel_3extra_gen0118", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a triangle ABC. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment AG. There is a line segment BH. There is a line segment CI. There is a line BC. Line AD is an altitude from vertex A of triangle ABC. Line BE is an altitude from vertex B of triangle ABC. Line AG is an angle bisector of angle CAB. Further, the length of line AD is equal to the length of line BE. Further, the area of triangle ABC is at most 12. Further, angle ABC is 60 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\nlineAD = scene.add.line_segment(A, D)\nlineBE = scene.add.line_segment(B, E)\nlineCF = scene.add.line_segment(C, F)\nlineAG = scene.add.line_segment(A, G)\nlineBH = scene.add.line_segment(B, H)\nlineCI = scene.add.line_segment(C, I)\nline_L = scene.add.line(B, C)\n\n### relationships\n\nscene.relate.is_altitude(lineAD, triangleABC, A)\nscene.relate.is_altitude(lineBE, triangleABC, B)\nscene.relate.angle_bisector(C, A, B, lineAG)\n\n### Extra relationships\n\nscene.constraint.eq(lineAD.length, lineBE.length)\nscene.constraint.leq(triangleABC.area, 12.0)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 60)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "lineAD": "line_segment(A, D)", "lineBE": "line_segment(B, E)", "lineCF": "line_segment(C, F)", "lineAG": "line_segment(A, G)", "lineBH": "line_segment(B, H)", "lineCI": "line_segment(C, I)", "line_L": "line(B, C)"}, "Rels": ["is_altitude(lineAD, triangleABC, A)", "is_altitude(lineBE, triangleABC, B)", "angle_bisector(C, A, B, lineAG)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": ["scene.constraint.eq(scene.get_object('lineAD').length, scene.get_object('lineBE').length)", "scene.constraint.leq(scene.get_object('triangleABC').area, 12.0)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 60)"], "possible_solution": {"points": {"A": [-1.1792954502431052, -2.52425750495918], "B": [-0.459959202735999, 1.2314636017206375], "C": [2.432922593218411, -1.2693604140413801], "D": [0.9864826723319314, -0.018948609537970142], "E": [0.6268142335437437, -1.8968095152252087], "F": [-3.628076517035822, 6.662034005706643], "G": [3.8085948794535387, 3.2455914861485105], "H": [-5.405210134507607, -9.12895283808346], "I": [0.5484969309647629, -8.723832635283404]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0121", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a scalene triangle ABC. There are line segments AD, BE, and DF. Line AD is an altitude of triangle ABC from vertex A. Line BE is a median of triangle ABC from vertex B. Angle BAC is acute. Further, length of line AD is equal to length of line BE, the slope of line DF is less than or equal to 0, and angle BAC is equal to 60 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ntriangleABC = scene.add.scalene_triangle(A, B, C)\nline_altitude_from_A = scene.add.line_segment(A, D)\nline_median_from_B = scene.add.line_segment(B, E)\nline_perpendicular_bisector = scene.add.line(D, F)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude_from_A, triangleABC, A)\nscene.relate.is_median(line_median_from_B, triangleABC, B)\nscene.relate.acute_angle(B, A, C)\n\n### Extra relationships\n\nscene.constraint.eq(line_altitude_from_A.length, line_median_from_B.length)\nscene.constraint.leq(line_perpendicular_bisector.slope, 0)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 60)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "scalene_triangle(A, B, C)", "line_altitude_from_A": "line_segment(A, D)", "line_median_from_B": "line_segment(B, E)", "line_perpendicular_bisector": "line(D, F)"}, "Rels": ["is_altitude(line_altitude_from_A, triangleABC, A)", "is_median(line_median_from_B, triangleABC, B)", "acute_angle(B, A, C)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_altitude_from_A').length, scene.get_object('line_median_from_B').length)", "scene.constraint.leq(scene.get_object('line_perpendicular_bisector').slope, 0)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 60)"], "possible_solution": {"points": {"A": [1.7110382882034099, 0.23370940690580186], "B": [3.7011087552346957, 4.367785272441295], "C": [6.285289308391301, 0.5772213902588542], "D": [4.993898167880513, 2.471743482623821], "E": [3.998161182611836, 0.4056120666217383], "F": [9.003042005515278, 0.6097184843358098]}, "circles": {}}}
{"unique_id": "1obj_3rel_3extra_gen0122", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There is a line segment BD. There is a line segment AC. There is a line segment EF. Line BD is a diameter of the circle. Line BD is perpendicular to line AC. Line EF is a chord of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BD, line_AC)\nscene.relate.is_chord(line_EF, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)"}, "Rels": ["is_diameter(line_BD, circle1)", "perpendicular(line_BD, line_AC)", "is_chord(line_EF, circle1)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.5422754124350161, 0.056647583053870625], "B": [-0.4732974494657663, -0.32555019623564224], "C": [1.9378707384096823, 0.5042571643467026], "D": [-0.6112532911247586, 0.4388453096229055], "E": [-0.2594814745507992, 0.32284394119516163], "F": [-0.8010524702058869, -0.23295118057687283]}, "circles": {"A": 0.388372304678149}}}
{"unique_id": "1obj_3rel_3extra_gen0124", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is an acute triangle ABC. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is a median of triangle ABC. Line BE is an altitude of triangle ABC. Line AD is perpendicular to line BE. Further, length of line AD is equal to length of line BE, area of triangle ABC is less than or equal to 12, and angle ABE is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ntriangleABC = scene.add.acute_triangle(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_median(line_AD, triangleABC, A)\nscene.relate.is_altitude(line_BE, triangleABC, B)\nscene.relate.perpendicular(line_AD, line_BE)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BE.length)\nscene.constraint.leq(triangleABC.area, 12.0)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('E')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "acute_triangle(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["is_median(line_AD, triangleABC, A)", "is_altitude(line_BE, triangleABC, B)", "perpendicular(line_AD, line_BE)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)", "scene.constraint.leq(scene.get_object('triangleABC').area, 12.0)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('E')), 90)"], "possible_solution": {"points": {"A": [0.37949728803909133, 1.8409802828363606], "B": [-6.161383580833569, -3.818615172559418], "C": [6.542637092483755, 7.413524829496261], "D": [0.19298269704069174, 1.7951772272669078], "E": [-6.0367495718469355, -3.9626565475523026], "F": [10.0, -4.397957395128071]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0004", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a major arc with center B, start point C, end point D. There is a line segment BC. There is a line segment CD. There is a line segment AD. Point B lies on the circle. Point C lies on the circle. Line segment BC is a diameter of the circle. Further, the length of line segment AD equals the length of line segment BC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\nsemicircle1 = scene.add.major_arc(B, C, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_AD = scene.add.line_segment(A, D)\n\n### relationships\n\nscene.relate.point_lies_on(B, circle1)\nscene.relate.point_lies_on(C, circle1)\nscene.relate.is_diameter(line_BC, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BC.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "semicircle1": "major_arc(B, C, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_AD": "line_segment(A, D)"}, "Rels": ["point_lies_on(B, circle1)", "point_lies_on(C, circle1)", "is_diameter(line_BC, circle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BC').length)"], "possible_solution": {"points": {"A": [-0.5420028622604859, -1.0820747742766021], "B": [0.05154165063403677, -2.012505244672703], "C": [-1.1355473701591028, -0.15164430326651968], "D": [-2.047001476785905, -2.6966839836399052]}, "circles": {"A": 1.1036285380331476}}}
{"unique_id": "2obj_3rel_1extra_gen0011", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a minor arc with center A from B to C. There is a quadrilateral with vertices D, E, F, G. There is a line segment DF. There is a line segment DE. The line DF is perpendicular to line DE. G is the midpoint of line DF. G lies on the minor arc with center A from B to C.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\narc1 = scene.add.minor_arc(A, B, C)\nquad1 = scene.add.quadrilateral(D, E, F, G)\nline_DF = scene.add.line_segment(D, F)\nline_DE = scene.add.line_segment(D, E)\n\n### relationships\n\nscene.relate.perpendicular(line_DF, line_DE)\nscene.relate.is_midpoint(G, line_DF)\nscene.relate.point_lies_on(G, arc1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"arc1": "minor_arc(A, B, C)", "quad1": "quadrilateral(D, E, F, G)", "line_DF": "line_segment(D, F)", "line_DE": "line_segment(D, E)"}, "Rels": ["perpendicular(line_DF, line_DE)", "is_midpoint(G, line_DF)", "point_lies_on(G, arc1)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [1.8533623685216747, 1.367487048058893], "B": [2.9973398476697395, 1.1538461000098463], "C": [0.8679357971654379, 1.9865681420350945], "D": [0.39370910582548957, 2.836230028536345], "E": [1.9276867461622973, 4.180744781905636], "F": [1.5935019824460046, 1.4673678183853236], "G": [0.9936055290965619, 2.151798906871772]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0013", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a rhomboid ABCD. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment AB. There is a line segment CD. Points A, E, and C are collinear. Line segment AC is a diameter of the circle. Line segment AC is perpendicular to line segment BD. Further, the length of line AB is equal to the length of line CD. Further, the length of line AC is equal to twice the radius of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nrhomboid1 = scene.add.rhomboid(A, B, C, D)\ncircle1 = scene.add.circle(E)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_AB = scene.add.line_segment(A, B)\nline_CD = scene.add.line_segment(C, D)\n\n### relationships\n\nscene.relate.collinear(A, E, C)\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.perpendicular(line_AC, line_BD)\n\n### Extra relationships\n\nscene.constraint.eq(line_AB.length, line_CD.length)\nscene.constraint.eq(line_AC.length, 2 * circle1.radius)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rhomboid1": "rhomboid(A, B, C, D)", "circle1": "circle(E)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_AB": "line_segment(A, B)", "line_CD": "line_segment(C, D)"}, "Rels": ["collinear(A, E, C)", "is_diameter(line_AC, circle1)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AB').length, scene.get_object('line_CD').length)", "scene.constraint.eq(scene.get_object('line_AC').length, 2 * scene.get_object('circle1').radius)"], "possible_solution": {"points": {"A": [-2.2209282910853982, -0.5006934325449434], "B": [-2.447788192064589, 1.2498692996134084], "C": [-0.7042139519596223, 1.5221177191796287], "D": [-0.47767270544233864, -0.2272786116341035], "E": [-1.4622540383021565, 0.5099838720893949]}, "circles": {"E": 1.2642757380384937}}}
{"unique_id": "2obj_3rel_1extra_gen0017", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a regular hexagon with vertices A, B, C, D, E, F. There is a circle with center G. There is a line segment AD. There is a line segment BE. Line AD and line BE intersect at point G. Line AD is a diameter of the circle. The circle is the circumcircle of the hexagon. Further, the length of line BE equals the diagonal of the hexagon.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\nhexagon1 = scene.add.regular_hexagon(A, B, C, D, E, F)\ncircle1 = scene.add.circle(G)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AD, line_BE, G)\nscene.relate.is_diameter(line_AD, circle1)\nscene.relate.is_circumcircle(circle1, hexagon1)\n\n### Extra relationships\n\nscene.constraint.eq(line_BE.length, hexagon1.diagonal)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"hexagon1": "regular_hexagon(A, B, C, D, E, F)", "circle1": "circle(G)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)"}, "Rels": ["lines_intersect_at(line_AD, line_BE, G)", "is_diameter(line_AD, circle1)", "is_circumcircle(circle1, hexagon1)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_BE').length, scene.get_object('hexagon1').diagonal)"], "possible_solution": {"points": {"A": [-20.0, 10.000000000000002], "B": [-15.000000000000002, 1.339745962155614], "C": [-5.000000000000001, 1.339745962155613], "D": [0.0, 9.999999999999998], "E": [-4.999999999999999, 18.660254037844386], "F": [-14.999999999999998, 18.660254037844386], "G": [-10.0, 10.0]}, "circles": {"G": 10.0}}}
{"unique_id": "2obj_3rel_1extra_gen0018", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, M, N, K. There is a triangle with vertices A, B, C. There is a parallelogram with vertices D, E, F, G. There is a line segment AM. There is a line segment BN. There is a line segment CK. Line AM is an altitude of triangle ABC from vertex A. Line BN is a median of triangle ABC from vertex B. Line AM is parallel to line BN.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, M, N, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"M\", \"N\", \"K\"])\n\ntriangle_ABC = scene.add.triangle(A, B, C)\nparallelogram_DEFG = scene.add.parallelogram(D, E, F, G)\nline_AM = scene.add.line_segment(A, M)\nline_BN = scene.add.line_segment(B, N)\nline_CK = scene.add.line_segment(C, K)\n\n### relationships\n\nscene.relate.is_altitude(line_AM, triangle_ABC, A)\nscene.relate.is_median(line_BN, triangle_ABC, B)\nscene.relate.parallel(line_AM, line_BN)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle_ABC": "Triangle(A, B, C)", "parallelogram_DEFG": "Parallelogram(D, E, F, G)", "line_AM": "line_segment(A, M)", "line_BN": "line_segment(B, N)", "line_CK": "line_segment(C, K)"}, "Rels": ["is_altitude(line_AM, triangle_ABC, A)", "is_median(line_BN, triangle_ABC, B)", "parallel(line_AM, line_BN)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "M", "N", "K"], "extra_rel": [], "possible_solution": {"points": {"A": [-3.8020446643507584, 6.073672176277852], "B": [-0.12632043844456775, 1.2075369700463163], "C": [2.803215737881656, 1.6215383468291655], "D": [-6.810673840603165, 7.6917764621612355], "E": [-8.88352824269755, 8.660266438026753], "F": [7.047657224605558, -7.296883178964585], "G": [9.120511720838381, -8.265373248630391], "M": [-3.0558564868636795, 0.7935353986041337], "N": [-0.4994144396612373, 3.84760488562894], "K": [-8.98815422226419, -4.482221126865494]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0031", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is an equilateral triangle ABC. There is a circle with center D. There is a line segment AD. There is a line segment BE. There is a line segment CF. Angle ADB is a right angle. Line AD is a radius of the circle. Line BE is an altitude of the triangle from vertex B. Further, length of line AD equals length of line BE and length of line CF is less than or equal to the diameter of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ntriangle1 = scene.add.equilateral_triangle(A, B, C)\ncircle1 = scene.add.circle(D)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.right_angle(A, D, B)\nscene.relate.is_radius(line_AD, circle1)\nscene.relate.is_altitude(line_BE, triangle1, B)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BE.length)\nscene.constraint.leq(line_CF.length, circle1.diameter)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "equilateral_triangle(A, B, C)", "circle1": "circle(D)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["right_angle(A, D, B)", "is_radius(line_AD, circle1)", "is_altitude(line_BE, triangle1, B)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)", "scene.constraint.leq(scene.get_object('line_CF').length, scene.get_object('circle1').diameter)"], "possible_solution": {"points": {"A": [2.691923155977547, -2.829326220093114], "B": [3.798023812300919, -2.838499919765921], "C": [3.2529182377508294, -1.8760018951962127], "D": [3.5175260020684576, -3.31516237329522], "E": [2.972420923142075, -2.352663949155742], "F": [3.6576107510221587, -1.932132606631556]}, "circles": {"D": 0.9579439866249179}}}
{"unique_id": "2obj_3rel_1extra_gen0033", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a right trapezoid ABCD. There is a circle with center E. There is a line segment AD. There is a line segment DC. There is a line segment AC. There is a line segment DE. Line AD is perpendicular to line DC. Line DE is a radius of the circle. Line AD extended intersects the circle at points D and F. Further, length of line AD equals length of line DC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ntrapezoid1 = scene.add.right_trapezoid(A, B, C, D)\ncircle1 = scene.add.circle(E)\nline_AD = scene.add.line_segment(A, D)\nline_DC = scene.add.line_segment(D, C)\nline_AC = scene.add.line_segment(A, C)\nline_DE = scene.add.line_segment(D, E)\n\n### relationships\n\nscene.relate.line_extension_intersects_circle_at(line_AD, circle1, D, F)\nscene.relate.is_radius(line_DE, circle1)\nscene.relate.perpendicular(line_AD, line_DC)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_DC.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "right_trapezoid(A, B, C, D)", "circle1": "circle(E)", "line_AD": "line_segment(A, D)", "line_DC": "line_segment(D, C)", "line_AC": "line_segment(A, C)", "line_DE": "line_segment(D, E)"}, "Rels": ["line_extension_intersects_circle_at(line_AD, circle1, D, F)", "is_radius(line_DE, circle1)", "perpendicular(line_AD, line_DC)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_DC').length)"], "possible_solution": {"points": {"A": [2.6586649356322116, 0.5729539843354772], "B": [0.9782591083184121, 0.2464907969645179], "C": [2.8182871629048063, 0.809552507893148], "D": [2.6201768333961786, 0.7710643557867712], "E": [1.7621814160646716, 1.8581464665257899], "F": [2.1507397094914085, 3.187404235344005]}, "circles": {"E": 1.384883995828574}}}
{"unique_id": "2obj_3rel_1extra_gen0036", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is an isosceles trapezoid ABCD. There is a major arc FG with center E. There is a line segment AB. There is a line segment CD. There is a line segment AC. There is a line segment BD. There is a line segment EF. Line AC intersects line BD at H. Trapezoid ABCD is reflected across line EF onto itself. Point H lies on line AC. Further, the length of line AB is equal to the length of line CD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntrapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)\narc1 = scene.add.major_arc(E, F, G)\nline_AB = scene.add.line_segment(A, B)\nline_CD = scene.add.line_segment(C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_BD, H)\nscene.relate.mirror_across_line(trapezoid1, trapezoid1, line_EF)\nscene.relate.point_lies_on(H, line_AC)\n\n### Extra relationships\n\nscene.constraint.eq(line_AB.length, line_CD.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "isosceles_trapezoid(A, B, C, D)", "arc1": "major_arc(E, F, G)", "line_AB": "line_segment(A, B)", "line_CD": "line_segment(C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["lines_intersect_at(line_AC, line_BD, H)", "mirror_across_line(trapezoid1, trapezoid1, line_EF)", "point_lies_on(H, line_AC)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AB').length, scene.get_object('line_CD').length)"], "possible_solution": {"points": {"A": [-9.47041755785377, 9.719130732842336], "B": [6.6987553793152115, -4.730229333552049], "C": [6.5474066623176705, -4.597471127305155], "D": [-9.621756121735496, 9.851899819004323], "E": [4.299851243834599, -2.58771823996204], "F": [7.3068583291228215, -5.274886598785778], "G": [2.4735339329893318, 1.007769344998385], "H": [-1.6881063600534463, 2.7633435208255244]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0039", "nl_description": "Diagram description: The diagram contains points A, B, C, O, D, E, F, G. There is a triangle ABC with vertices A, B, C. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD intersects line BE at point G. Line AD is an altitude of triangle ABC from vertex A. Line BE is an altitude of triangle ABC from vertex B. Line CF is an altitude of triangle ABC from vertex C. The circle with center O is the circumcircle of triangle ABC. Further, the area of triangle ABC is equal to one-fourth the area of circle O.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"O\", \"D\", \"E\", \"F\", \"G\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\ncircleO = scene.add.circle(O)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AD, line_BE, G)\nscene.relate.is_altitude(line_AD, triangleABC, A)\nscene.relate.is_circumcircle(circleO, triangleABC)\n\n### Extra relationships\n\nscene.constraint.eq(triangleABC.area, circleO.area / 4)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "Triangle(A, B, C)", "circleO": "Circle(O)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["lines_intersect_at(line_AD, line_BE, G)", "is_altitude(line_AD, triangleABC, A)", "is_circumcircle(circleO, triangleABC)"], "Points": ["A", "B", "C", "O", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangleABC').area, scene.get_object('circleO').area / 4)"], "possible_solution": {"points": {"A": [2.245347138977053, 0.8629813191130374], "B": [-1.0399719740485873, -1.6614864146679358], "C": [2.350970621220491, -7.4512803995079055], "O": [2.8220376316217197, -3.287494501162145], "D": [-1.3017721874209434, -1.2144808710892314], "E": [0.020013907142532955, -0.12110188466968418], "F": [0.5221541314184573, 0.47659856936230105], "G": [-0.3479715971779239, -0.6558628637742002]}, "circles": {"O": 4.190348563193061}}}
{"unique_id": "2obj_3rel_1extra_gen0040", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a right isosceles triangle with vertices B, C, D. There is a line segment BC. There is a line segment CD. There is a line segment BD. There is a line segment AD. There is a line segment AC. Line segment BC is rotated 90 degrees around point C to form line segment CD. Line segment BC is a chord of the circle. Line segment AC is a radius of the circle. Further, the length of line BC is equal to the length of line CD. Further, the length of line BC is equal to 2 times the area of the circle divided by (3.14159 times 2).", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.right_isosceles_triangle(B, C, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline BD = scene.add.line_segment(B, D)\nline_AD = scene.add.line_segment(A, D)\nline_AC = scene.add.line_segment(A, C)\n\n### relationships\n\nscene.relate.rotation_around_point(line_BC, line_CD, C, 90)\nscene.relate.is_chord(line_BC, circle1)\nscene.relate.is_radius(line_AC, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(line_BC.length, line_CD.length)\nscene.constraint.eq(line_BC.length, 2 * circle1.area / (3.14159 * 2))\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "right_isosceles_triangle(B, C, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line BD": "line_segment(B, D)", "line_AD": "line_segment(A, D)", "line_AC": "line_segment(A, C)"}, "Rels": ["rotation_around_point(line_BC, line_CD, C, 90)", "is_chord(line_BC, circle1)", "is_radius(line_AC, circle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_BC').length, scene.get_object('line_CD').length)", "scene.constraint.eq(scene.get_object('line_BC').length, 2 * scene.get_object('circle1').area / (3.14159 * 2))"], "possible_solution": {"points": {"A": [-1.4206359284041714, -1.8922063161193219], "B": [-0.6236852259139054, -2.215640734817097], "C": [-0.6673103158064126, -1.4771872962073582], "D": [-1.4057637272711978, -1.5208123682566246]}, "circles": {"A": 0.8600815562302212}}}
{"unique_id": "2obj_3rel_1extra_gen0041", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a rhombus with vertices A, B, C, D. There is a major arc with center E, start point F, and end point G. There is a line segment AC. There is a line segment BD. There is a line segment EF. Line segment AC is parallel to line segment EF. Line segment BD is perpendicular to line segment EF. Point F lies on the major arc.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\nrhombus1 = scene.add.rhombus(A, B, C, D)\nsemicircle1 = scene.add.major_arc(E, F, G)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.parallel(line_AC, line_EF)\nscene.relate.perpendicular(line_BD, line_EF)\nscene.relate.point_lies_on(F, semicircle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rhombus1": "rhombus(A, B, C, D)", "semicircle1": "major_arc(E, F, G)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["parallel(line_AC, line_EF)", "perpendicular(line_BD, line_EF)", "point_lies_on(F, semicircle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [0.22954552473131692, -3.1601850453414504], "B": [-2.491570551446355, -0.941746150796746], "C": [1.007401176968923, -0.6534049578012158], "D": [3.7285172465348757, -2.8718438529844232], "E": [-1.2864949216297257, -2.00655243983619], "F": [0.09607417787310121, 2.4490257229842975], "G": [-2.3954757600806142, 2.5248751003807657]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0055", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a rectangle with A, B, C, D. There is a right triangle with E, F, G. There is a line segment AC. There is a line segment EF. There is a line segment FG. There is a line segment EG. Points A, C, E are collinear. Line AC is perpendicular to line EF. Line FG is an altitude of right triangle EFG from vertex F to the hypotenuse EG.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\nright_triangle1 = scene.add.right_triangle(E, F, G)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\nline_FG = scene.add.line_segment(F, G)\nlineEG = scene.add.line_segment(E, G)\n\n### relationships\n\nscene.relate.collinear(A, C, E)\nscene.relate.perpendicular(line_AC, line_EF)\nscene.relate.is_altitude(line_FG, right_triangle1, F)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "right_triangle1": "right_triangle(E, F, G)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)", "line_FG": "line_segment(F, G)", "lineEG": "line_segment(E, G)"}, "Rels": ["collinear(A, C, E)", "perpendicular(line_AC, line_EF)", "is_altitude(line_FG, right_triangle1, F)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [-6.340846127395391, -3.4351850959438135], "B": [-0.781561393819733, -6.36587391747021], "C": [-0.60281172524579, -6.026800541152594], "D": [-6.162096719288207, -3.0961114649606927], "E": [-0.3750333907823563, -6.129677750250283], "F": [6.391224355080886, 8.851333207753417], "G": [6.209216153559748, 8.933528461299323]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0061", "nl_description": "Diagram description: The diagram contains points A, B, C, O, D, E, F.\nThere is a triangle with vertices A, B, C.\nThere is a circle with center O.\nThere is a line segment AD.\nThere is a line segment BE.\nThere is a line segment CF.\nLine AD is a median of triangle ABC.\nThe circle with center O is the circumcircle of triangle ABC.\nLine AD is perpendicular to line BE.\nFurther, the length of line AD is equal to the length of line BE and the area of triangle ABC is 12.0.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"O\", \"D\", \"E\", \"F\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\ncircleO = scene.add.circle(O)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_median(line_AD, triangleABC, A)\nscene.relate.is_circumcircle(circleO, triangleABC)\nscene.relate.perpendicular(line_AD, line_BE)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BE.length)\nscene.constraint.eq(triangleABC.area, 12.0)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "circleO": "circle(O)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["is_median(line_AD, triangleABC, A)", "is_circumcircle(circleO, triangleABC)", "perpendicular(line_AD, line_BE)"], "Points": ["A", "B", "C", "O", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)", "scene.constraint.eq(scene.get_object('triangleABC').area, 12.0)"], "possible_solution": {"points": {"A": [3.1794244416062654, -0.9544728764400469], "B": [-0.3467874366270521, 3.257766925089883], "C": [1.3356422006740705, -5.558151682606375], "O": [-1.8730564084316765, -1.602003053607088], "D": [0.4944273983442532, -1.150192216945279], "E": [-0.15106815788603503, 0.5727707075780232], "F": [7.377775119275979, 8.522103738213884]}, "circles": {"O": 5.093806184503651}}}
{"unique_id": "2obj_3rel_1extra_gen0063", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a major arc with center A, start point B, and end point C. There is a scalene triangle with vertices D, E, F. There is a line segment DE. There is a line segment EF. There is a line segment FD. There is a line segment FG. Point G lies on the major arc with center A, start point B, and end point C. Line segment FG is perpendicular to line segment FD. Line segment FG is an altitude of the scalene triangle DEF from vertex F.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\nsemicircle1 = scene.add.major_arc(A, B, C)\ntriangle1 = scene.add.scalene_triangle(D, E, F)\nline_DE = scene.add.line_segment(D, E)\nline_EF = scene.add.line_segment(E, F)\nline_FD = scene.add.line_segment(F, D)\nline_perp = scene.add.line_segment(F, G)\n\n### relationships\n\nscene.relate.point_lies_on(G, semicircle1)\nscene.relate.perpendicular(line_perp, line_FD)\nscene.relate.is_altitude(line_perp, triangle1, F)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"semicircle1": "major_arc(A, B, C)", "triangle1": "scalene_triangle(D, E, F)", "line_DE": "line_segment(D, E)", "line_EF": "line_segment(E, F)", "line_FD": "line_segment(F, D)", "line_perp": "line_segment(F, G)"}, "Rels": ["point_lies_on(G, semicircle1)", "perpendicular(line_perp, line_FD)", "is_altitude(line_perp, triangle1, F)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [7.642805403167586, 8.700965557997154], "B": [9.39749569226807, -8.321916612414158], "C": [-9.470244989306988, 8.669933242950995], "D": [-9.846546141586865, 8.834762440446868], "E": [8.521389282007213, -9.725675848380993], "F": [7.072964518347489, -8.54622254700947], "G": [7.216191448826622, -8.406794462147932]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0065", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a triangle ABC. There is a quadrilateral ABCD. There is a line segment AC. There is a line segment BD. E is the midpoint of line AC. Line AC is perpendicular to line BD. Line AC intersects line BD at point F. Further, the length of line AC is equal to the length of line BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\nquadrilateralABCD = scene.add.quadrilateral(A, B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\n\n### relationships\n\nscene.relate.is_midpoint(E, line_AC)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.lines_intersect_at(line_AC, line_BD, F)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "quadrilateralABCD": "quadrilateral(A, B, C, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)"}, "Rels": ["is_midpoint(E, line_AC)", "perpendicular(line_AC, line_BD)", "lines_intersect_at(line_AC, line_BD, F)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)"], "possible_solution": {"points": {"A": [2.0033461468098204, -4.648272820113974], "B": [1.464233576944619, -4.728015760736211], "C": [-0.07302471917458685, -2.2462581729470625], "D": [3.8662482207949487, -2.6516448876338066], "E": [0.9651607625826867, -3.4472654816873427], "F": [1.8122370665888812, -4.427191507266672]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0075", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a quadrilateral with vertices A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment AB. There is a line segment CD. Points A, E, and C are collinear. The line segment AC is a diameter of the circle. Line segment AB is perpendicular to line segment CD. Further, the length of line AB is equal to the length of line CD, and the angle ABC is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nquadrilateral1 = scene.add.quadrilateral(A, B, C, D)\ncircle1 = scene.add.circle(E)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_AB = scene.add.line_segment(A, B)\nline_CD = scene.add.line_segment(C, D)\n\n### relationships\n\nscene.relate.collinear(A, E, C)\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.perpendicular(line_AB, line_CD)\n\n### Extra relationships\n\nscene.constraint.eq(line_AB.length, line_CD.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"quadrilateral1": "quadrilateral(A, B, C, D)", "circle1": "circle(E)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_AB": "line_segment(A, B)", "line_CD": "line_segment(C, D)"}, "Rels": ["collinear(A, E, C)", "is_diameter(line_AC, circle1)", "perpendicular(line_AB, line_CD)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AB').length, scene.get_object('line_CD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [-2.629856784952943, -1.3936997532816333], "B": [0.4223762814445624, 2.706548175050386], "C": [-2.4752967251011535, 4.86358197703594], "D": [1.6249511767483653, 1.8113489531388094], "E": [-2.5525767572539357, 1.7349411142549296]}, "circles": {"E": 3.129595159194952}}}
{"unique_id": "2obj_3rel_1extra_gen0080", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a right triangle BCD. There is a line segment BC. There is a line segment CD. There is a line segment BD. Line BC intersects the circle at points B and C. Line BC is a chord of the circle. Right angle at C between line segments CD and CB. Further, the area of right triangle BCD equals one-fourth the area of the circle with center A.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.right_triangle(B, C, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_BD = scene.add.line_segment(B, D)\n\n### relationships\n\nscene.relate.line_intersects_circle_at(line_BC, circle1, B, C)\nscene.relate.is_chord(line_BC, circle1)\nscene.relate.right_angle(D, C, B)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.area, circle1.area / 4)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "right_triangle(B, C, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_BD": "line_segment(B, D)"}, "Rels": ["line_intersects_circle_at(line_BC, circle1, B, C)", "is_chord(line_BC, circle1)", "right_angle(D, C, B)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('circle1').area / 4)"], "possible_solution": {"points": {"A": [2.9052768854281013, -1.9956817923864432], "B": [2.49574471302029, -2.6117476643975355], "C": [2.2573861739841425, -2.3527411583386995], "D": [0.4603743037768022, -4.006495425413686]}, "circles": {"A": 0.7397660198253597}}}
{"unique_id": "2obj_3rel_1extra_gen0082", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a rectangle with points A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment AB. There is a line segment BC. Line AC intersects the circle at points A and C. Line AC is a diameter of the circle. Line AB is perpendicular to line BC. Further, the area of rectangle ABCD equals the area of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\ncircle1 = scene.add.circle(E)\nline_AC = scene.add.line_segment(A, C)\nline BD = scene.add.line_segment(B, D)\nline_AB = scene.add.line_segment(A, B)\nline_BC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.line_intersects_circle_at(line_AC, circle1, A, C)\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.perpendicular(line_AB, line_BC)\n\n### Extra relationships\n\nscene.constraint.eq(rectangle1.area, circle1.area)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "circle1": "circle(E)", "line_AC": "line_segment(A, C)", "line BD": "line_segment(B, D)", "line_AB": "line_segment(A, B)", "line_BC": "line_segment(B, C)"}, "Rels": ["line_intersects_circle_at(line_AC, circle1, A, C)", "is_diameter(line_AC, circle1)", "perpendicular(line_AB, line_BC)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('rectangle1').area, scene.get_object('circle1').area)"], "possible_solution": {"points": {"A": [-3.562620126572567, 0.48940872435241944], "B": [-3.82778282023589, 0.41171634763704873], "C": [-3.7361094386133615, 0.1510600773439574], "D": [-3.477589745977895, 0.23215802421621967], "E": [-3.6513860607886985, 0.3212707629885001]}, "circles": {"E": 0.16648944007974167}}}
{"unique_id": "2obj_3rel_1extra_gen0086", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is an equilateral triangle with vertices B, C, D. There is a line segment BC. There is a line segment CD. There is a line segment DB. There is a line segment AD. There is a line segment AC. There is a line segment AB. The circle is the circumcircle of the equilateral triangle BCD. Line AB is a radius of the circle. Point B lies on the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.equilateral_triangle(B, C, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_DB = scene.add.line_segment(D, B)\nline_AD = scene.add.line_segment(A, D)\nline_AC = scene.add.line_segment(A, C)\nline_AB = scene.add.line_segment(A, B)\n\n### relationships\n\nscene.relate.is_circumcircle(circle1, triangle1)\nscene.relate.is_radius(line_AB, circle1)\nscene.relate.point_lies_on(B, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "equilateral_triangle(B, C, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_DB": "line_segment(D, B)", "line_AD": "line_segment(A, D)", "line_AC": "line_segment(A, C)", "line_AB": "line_segment(A, B)"}, "Rels": ["is_circumcircle(circle1, triangle1)", "is_radius(line_AB, circle1)", "point_lies_on(B, circle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": [], "possible_solution": {"points": {"A": [-1.133102523154442, -0.9896005391546037], "B": [-0.8505928367049341, 0.3835516972103044], "C": [-0.08517263857965653, -1.9208371873729388], "D": [-2.4635420613270202, -1.4315160287415771]}, "circles": {"A": 1.4019125473555607}}}
{"unique_id": "2obj_3rel_1extra_gen0096", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a right triangle BCD. There is a line segment BC. There is a line segment CD. There is a line segment BD. There is a line segment AD. Line BC is perpendicular to line CD. Line BD is a chord of the circle. Point D lies on the circle. Further, the inradius of the right triangle BCD is 1.0. Further, the length of line BD is less than or equal to 6.0.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.right_triangle(B, C, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_BD = scene.add.line_segment(B, D)\nline_AD = scene.add.line_segment(A, D)\n\n### relationships\n\nscene.relate.perpendicular(line_BC, line_CD)\nscene.relate.is_chord(line_BD, circle1)\nscene.relate.point_lies_on(D, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.inradius, 1.0)\nscene.constraint.leq(line_BD.length, 6.0)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "right_triangle(B, C, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_BD": "line_segment(B, D)", "line_AD": "line_segment(A, D)"}, "Rels": ["perpendicular(line_BC, line_CD)", "is_chord(line_BD, circle1)", "point_lies_on(D, circle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').inradius, 1.0)", "scene.constraint.leq(scene.get_object('line_BD').length, 6.0)"], "possible_solution": {"points": {"A": [9.118768679138398, -0.21176592409640443], "B": [0.6667395205291882, -2.09100145223368], "C": [3.227708695027182, 0.12900219548746], "D": [0.9747010148845378, 2.7280444339700325]}, "circles": {"A": 8.65842497606689}}}
{"unique_id": "2obj_3rel_1extra_gen0100", "nl_description": "Diagram description: The diagram contains points A, B, C, D, H, M, N. There is a triangle ABC. There is a major arc ADB. There is a line segment AH. There is a line segment MN. H is the orthocenter of triangle ABC. line segment AH is perpendicular to line segment MN. point H lies on line segment MN.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, H, M, N = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"H\", \"M\", \"N\"])\n\ntriangle_ABC = scene.add.triangle(A, B, C)\nsemicircle_ADB = scene.add.major_arc(A, D, B)\nline_altitude = scene.add.line_segment(A, H)\nline_perp_bisector = scene.add.line_segment(M, N)\n\n### relationships\n\nscene.relate.is_orthocenter(H, triangle_ABC)\nscene.relate.perpendicular(line_altitude, line_perp_bisector)\nscene.relate.point_lies_on(H, line_perp_bisector)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle_ABC": "triangle(A, B, C)", "semicircle_ADB": "major_arc(A, D, B)", "line_altitude": "line_segment(A, H)", "line_perp_bisector": "line_segment(M, N)"}, "Rels": ["is_orthocenter(H, triangle_ABC)", "perpendicular(line_altitude, line_perp_bisector)", "point_lies_on(H, line_perp_bisector)"], "Points": ["A", "B", "C", "D", "H", "M", "N"], "extra_rel": [], "possible_solution": {"points": {"A": [0.8024069259430161, -1.100651563536721], "B": [1.0025055073138935, 2.509254261489706], "C": [-0.9254212816902895, 0.1695007182519168], "D": [-0.9334149166907499, 2.0708436707580242], "H": [-0.7256235233615248, 0.15842581351080484], "M": [-0.127849738459818, 0.883890799406125], "N": [-1.4939097348565538, -0.7739749802444731]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0107", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is an isosceles trapezoid ABCD. There is a minor arc FG with center E. There is a line segment AB. There is a line segment CD. There is a line segment EF. There is a line segment EG. There is an obtuse angle at D formed by points A, D, and C. The trapezoid is symmetric about line AB. Point F lies on the minor arc FG. Further, length of line AB is equal to length of line CD and the area of the trapezoid is less than or equal to 20.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntrapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)\narc1 = scene.add.minor_arc(E, F, G)\nline_AB = scene.add.line_segment(A, B)\nline_CD = scene.add.line_segment(C, D)\nline EF = scene.add.line_segment(E, F)\nline EG = scene.add.line_segment(E, G)\n\n### relationships\n\nscene.relate.obtuse_angle(A, D, C)\nscene.relate.mirror_across_line(trapezoid1, trapezoid1, line_AB)\nscene.relate.point_lies_on(F, arc1)\n\n### Extra relationships\n\nscene.constraint.eq(line_AB.length, line_CD.length)\nscene.constraint.leq(trapezoid1.area, 20)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "isosceles_trapezoid(A, B, C, D)", "arc1": "minor_arc(E, F, G)", "line_AB": "line_segment(A, B)", "line_CD": "line_segment(C, D)", "line EF": "line_segment(E, F)", "line EG": "line_segment(E, G)"}, "Rels": ["obtuse_angle(A, D, C)", "mirror_across_line(trapezoid1, trapezoid1, line_AB)", "point_lies_on(F, arc1)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AB').length, scene.get_object('line_CD').length)", "scene.constraint.leq(scene.get_object('trapezoid1').area, 20)"], "possible_solution": {"points": {"A": [9.328119115361437, -2.821061934435527], "B": [-9.372843429254559, 8.393547815752788], "C": [-9.928106816575745, 8.724399123128727], "D": [8.772856581598427, -2.4902116973565893], "E": [0.45360424617979606, 2.8505895178993055], "F": [-1.0158031176185323, -0.9739895368653604], "G": [-0.46781371755107615, -1.1415969720026755]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0125", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a rhomboid with vertices A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment AB. There is a line segment BC. Points A, E, and C are collinear. Line segment AC is a diameter of the circle. Line segment AC is perpendicular to line segment BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nrhomboid1 = scene.add.rhomboid(A, B, C, D)\ncircle1 = scene.add.circle(E)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_AB = scene.add.line_segment(A, B)\nline_BC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.collinear(A, E, C)\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.perpendicular(line_AC, line_BD)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rhomboid1": "rhomboid(A, B, C, D)", "circle1": "circle(E)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_AB": "line_segment(A, B)", "line_BC": "line_segment(B, C)"}, "Rels": ["collinear(A, E, C)", "is_diameter(line_AC, circle1)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [3.2443171092639274, -2.1007472441549426], "B": [3.230077150841898, -1.6682070392136825], "C": [2.88346954859584, -1.9274038016172532], "D": [2.897743822930944, -2.3599182458804], "E": [3.0638928135372256, -2.0140681877351243]}, "circles": {"E": 0.20017809061837083}}}
{"unique_id": "2obj_3rel_1extra_gen0129", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, M, N. There is an isosceles triangle ABC. There is a minor arc with center D and endpoints E and F. There is a line segment AM. There is a line segment BC. N is the orthocenter of triangle ABC. line AM is an altitude of triangle ABC from vertex A. M lies on line BC. Further, the inradius of triangle ABC equals the radius of the minor arc with center D and endpoints E and F.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, M, N = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"M\", \"N\"])\n\ntriangleABC = scene.add.isosceles_triangle(A, B, C)\narcDEF = scene.add.minor_arc(D, E, F)\nline_AM = scene.add.line_segment(A, M)\nline_BC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.is_orthocenter(N, triangleABC)\nscene.relate.is_altitude(line_AM, triangleABC, A)\nscene.relate.point_lies_on(M, line_BC)\n\n### Extra relationships\n\nscene.constraint.eq(triangleABC.inradius, arcDEF.radius)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "isosceles_triangle(A, B, C)", "arcDEF": "minor_arc(D, E, F)", "line_AM": "line_segment(A, M)", "line_BC": "line_segment(B, C)"}, "Rels": ["is_orthocenter(N, triangleABC)", "is_altitude(line_AM, triangleABC, A)", "point_lies_on(M, line_BC)"], "Points": ["A", "B", "C", "D", "E", "F", "M", "N"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangleABC').inradius, scene.get_object('arcDEF').radius)"], "possible_solution": {"points": {"A": [-1.820559422842501, -0.3431467698607907], "B": [1.1880729984933318, -1.1231737836004163], "C": [-0.60656231433224, -3.6608095657681092], "D": [2.2220557665331118, -2.325810105732441], "E": [1.3323229682245612, -2.0665805274474964], "F": [1.6912474127221315, -1.5661609041676974], "M": [0.552730592935256, -2.021555546314196], "N": [-0.06779020617211239, -1.582718475648451]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0133", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a trapezoid ABCD. There is a minor arc FG with center E. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment EG. Points A, E, and G are collinear. Point F lies on the minor arc FG. Line segment AC is perpendicular to line segment BD. Further, the area of trapezoid ABCD equals the area of minor arc FG. Further, the angle FEG measures 60 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntrapezoid1 = scene.add.trapezoid(A, B, C, D)\nminor_arc1 = scene.add.minor_arc(E, F, G)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline EF = scene.add.line_segment(E, F)\nline EG = scene.add.line_segment(E, G)\n\n### relationships\n\nscene.relate.collinear(A, E, G)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.point_lies_on(F, minor_arc1)\n\n### Extra relationships\n\nscene.constraint.eq(trapezoid1.area, minor_arc1.area)\nscene.constraint.eq(scene.angle(scene.get_object('F'), scene.get_object('E'), scene.get_object('G')), 60)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "trapezoid(A, B, C, D)", "minor_arc1": "minor_arc(E, F, G)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line EF": "line_segment(E, F)", "line EG": "line_segment(E, G)"}, "Rels": ["collinear(A, E, G)", "perpendicular(line_AC, line_BD)", "point_lies_on(F, minor_arc1)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('trapezoid1').area, scene.get_object('minor_arc1').area)", "scene.constraint.eq(scene.angle(scene.get_object('F'), scene.get_object('E'), scene.get_object('G')), 60)"], "possible_solution": {"points": {"A": [-0.7500963154973908, 3.3024813782518465], "B": [-2.022889078212349, -1.571677433172988], "C": [-3.1794420183525314, -0.22986912921601257], "D": [-3.3004004238609377, -0.6930792571517274], "E": [-1.4372496365936813, -0.20711405707684832], "F": [0.4619262352247533, -1.8625846981007546], "G": [-1.9213413292241759, -2.6795839161124064]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0145", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a circle with center E. There is a quadrilateral ABCD. There is a line segment AC. There is a line segment BD. There is a line segment AB. Line AC is a chord of the circle. Line AC is perpendicular to line BD. Line AB is a diameter of the circle. Further, the area of quadrilateral ABCD equals the area of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nquadrilateral1 = scene.add.quadrilateral(A, B, C, D)\ncircle1 = scene.add.circle(E)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_AB = scene.add.line_segment(A, B)\n\n### relationships\n\nscene.relate.is_chord(line_AC, circle1)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.is_diameter(line_AB, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(quadrilateral1.area, circle1.area)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"quadrilateral1": "quadrilateral(A, B, C, D)", "circle1": "circle(E)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_AB": "line_segment(A, B)"}, "Rels": ["is_chord(line_AC, circle1)", "perpendicular(line_AC, line_BD)", "is_diameter(line_AB, circle1)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('quadrilateral1').area, scene.get_object('circle1').area)"], "possible_solution": {"points": {"A": [1.8565625217688477, 0.2743022303678448], "B": [0.4534736027947839, 0.8399289087922441], "C": [0.4059010032598043, 0.4523691327512236], "D": [0.7531444358483251, 3.281263762824414], "E": [1.1550180253664182, 0.5571155487318612]}, "circles": {"E": 0.7564046612873904}}}
{"unique_id": "2obj_3rel_1extra_gen0146", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a major arc BC. There are line segments BD, CD, and AD. Line BD is a chord of the circle. Angle BDC is a right angle. The circle is congruent to the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\nmajor_arc1 = scene.add.major_arc(A, B, C)\nline_BD = scene.add.line_segment(B, D)\nline_CD = scene.add.line_segment(C, D)\nline_AD = scene.add.line_segment(A, D)\n\n### relationships\n\nscene.relate.congruent(circle1, circle1)\nscene.relate.is_chord(line_BD, circle1)\nscene.relate.right_angle(B, D, C)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "major_arc1": "major_arc(A, B, C)", "line_BD": "line_segment(B, D)", "line_CD": "line_segment(C, D)", "line_AD": "line_segment(A, D)"}, "Rels": ["congruent(circle1, circle1)", "is_chord(line_BD, circle1)", "right_angle(B, D, C)"], "Points": ["A", "B", "C", "D"], "extra_rel": [], "possible_solution": {"points": {"A": [0.07887915401373201, -2.0770927545855735], "B": [-1.768491301398502, -2.3527898749236096], "C": [1.926249609963486, -1.8013956061802439], "D": [1.259519807838931, -3.5244607550578384]}, "circles": {"A": 1.8678293517440867}}}
{"unique_id": "2obj_3rel_1extra_gen0147", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a minor arc BC on that circle. There are line segments BC, AD, and CD. The circle is congruent to itself. Line BC is a chord of the circle. Line AD is perpendicular to line CD. Further, the length of line BC is equal to the length of line AD and angle BAD is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\nminor_arc1 = scene.add.minor_arc(A, B, C)\nline_BC = scene.add.line_segment(B, C)\nline_AD = scene.add.line_segment(A, D)\nline_CD = scene.add.line_segment(C, D)\n\n### relationships\n\nscene.relate.congruent(circle1, circle1)\nscene.relate.is_chord(line_BC, circle1)\nscene.relate.perpendicular(line_AD, line_CD)\n\n### Extra relationships\n\nscene.constraint.eq(line_BC.length, line_AD.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "minor_arc1": "minor_arc(A, B, C)", "line_BC": "line_segment(B, C)", "line_AD": "line_segment(A, D)", "line_CD": "line_segment(C, D)"}, "Rels": ["congruent(circle1, circle1)", "is_chord(line_BC, circle1)", "perpendicular(line_AD, line_CD)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_BC').length, scene.get_object('line_AD').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 90)"], "possible_solution": {"points": {"A": [-2.8687514989296408, -1.0257283892175024], "B": [2.841523964185174, 1.4836837855507736], "C": [2.735141439433411, 1.7130271397102406], "D": [-2.970464201505111, -0.7942767516626598]}, "circles": {"A": 6.2373386398684545}}}
{"unique_id": "2obj_3rel_1extra_gen0159", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a circle with center A. There is a circle with center B. There is a line segment CD. There is a line segment AB. There is a line segment EF. Line segment CD intersects line segment AB at point G. Line segment CD is a chord of the circle with center A. Line segment EF is tangent to the circle with center B at point F. Further, the areas of the circles with centers A and B are equal.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ncircle1 = scene.add.circle(A)\ncircle2 = scene.add.circle(B)\nline_CD = scene.add.line_segment(C, D)\nline_AB = scene.add.line_segment(A, B)\nline EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_CD, line_AB, G)\nscene.relate.is_chord(line_CD, circle1)\nscene.relate.tangent_to_circle(line EF, circle2, F)\n\n### Extra relationships\n\nscene.constraint.eq(circle1.area, circle2.area)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "circle2": "circle(B)", "line_CD": "line_segment(C, D)", "line_AB": "line_segment(A, B)", "line EF": "line_segment(E, F)"}, "Rels": ["lines_intersect_at(line_CD, line_AB, G)", "is_chord(line_CD, circle1)", "tangent_to_circle(line EF, circle2, F)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('circle1').area, scene.get_object('circle2').area)"], "possible_solution": {"points": {"A": [-0.319957733500781, 1.3322251340340248], "B": [1.7985067268088635, -1.323402578348358], "C": [-0.3060577906112217, 0.9915591444227319], "D": [0.020272865294646922, 1.3543538987831338], "E": [-1.2798732182674863, 0.07401011090466396], "F": [1.6269836409292042, -1.6180660368347197], "G": [-0.1693977954552539, 1.1434887680952197]}, "circles": {"A": 0.34094940858684225, "B": 0.34094945152144684}}}
{"unique_id": "2obj_3rel_1extra_gen0160", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a trapezoid ABCD. There is a circle with center E. There is a line segment AB. There is a line segment CD. There is a line segment AC. There is a line segment AD. Line AC intersects the circle at points A and C. Line AB is perpendicular to line AD. Line AC is a diameter of the circle. Further, the length of line AD is equal to the length of line AB. Further, angle ABC is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ntrapezoid1 = scene.add.trapezoid(A, B, C, D)\ncircle1 = scene.add.circle(E)\nline_AB = scene.add.line_segment(A, B)\nline_CD = scene.add.line_segment(C, D)\nline_AC = scene.add.line_segment(A, C)\nline_AD = scene.add.line_segment(A, D)\n\n### relationships\n\nscene.relate.line_intersects_circle_at(line_AC, circle1, A, C)\nscene.relate.perpendicular(line_AB, line_AD)\nscene.relate.is_diameter(line_AC, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_AB.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "trapezoid(A, B, C, D)", "circle1": "circle(E)", "line_AB": "line_segment(A, B)", "line_CD": "line_segment(C, D)", "line_AC": "line_segment(A, C)", "line_AD": "line_segment(A, D)"}, "Rels": ["line_intersects_circle_at(line_AC, circle1, A, C)", "perpendicular(line_AB, line_AD)", "is_diameter(line_AC, circle1)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_AB').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [-0.3286992794728645, 0.25998841111755516], "B": [-4.426099510918487, 1.1150543460263014], "C": [-3.5710335778172553, 5.212454563925944], "D": [0.5263666411096877, 4.357388607576358], "E": [-1.9498664519772588, 2.736221480457761]}, "circles": {"E": 2.959715062560386}}}
{"unique_id": "2obj_3rel_1extra_gen0165", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a rectangle with points A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment AB. There is a line segment BC. Points A, E, and C are collinear. Line segment AC is a diameter of the circle. Line AB is perpendicular to line BC. Further, the diameter of the circle is equal to the length of line BC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\ncircle1 = scene.add.circle(E)\nline_AC = scene.add.line_segment(A, C)\nline BD = scene.add.line_segment(B, D)\nline_AB = scene.add.line_segment(A, B)\nline_BC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.collinear(A, E, C)\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.perpendicular(line_AB, line_BC)\n\n### Extra relationships\n\nscene.constraint.eq(circle1.diameter, line_BC.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "circle1": "circle(E)", "line_AC": "line_segment(A, C)", "line BD": "line_segment(B, D)", "line_AB": "line_segment(A, B)", "line_BC": "line_segment(B, C)"}, "Rels": ["collinear(A, E, C)", "is_diameter(line_AC, circle1)", "perpendicular(line_AB, line_BC)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('circle1').diameter, scene.get_object('line_BC').length)"], "possible_solution": {"points": {"A": [-4.525409778426829, -9.420844629293077], "B": [-4.663855483738467, -9.274845231240272], "C": [8.726814784882274, 3.4228976269050024], "D": [8.865259873730412, 3.276897521210077], "E": [2.1007026269778555, -2.998973475431842]}, "circles": {"E": 9.227444517039654}}}
{"unique_id": "2obj_3rel_1extra_gen0172", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, G. There is a right triangle ABC with vertices A, B, C. There is a minor arc with center D, starting at E and ending at G. There is a line segment AB. There is a line segment BC. There is a line segment AC. There is a line segment DG. Line AB is parallel to line DG. Line BC is an altitude of triangle ABC from vertex B. Point E lies on the minor arc with center D. Further, the length of line AB is equal to the length of line DG and the central angle of the minor arc is less than or equal to 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"G\"])\n\ntriangleABC = scene.add.right_triangle(A, B, C)\narcDEG = scene.add.minor_arc(D, E, G)\nlineAB = scene.add.line_segment(A, B)\nlineBC = scene.add.line_segment(B, C)\nlineAC = scene.add.line_segment(A, C)\nlineDG = scene.add.line_segment(D, G)\n\n### relationships\n\nscene.relate.parallel(lineAB, lineDG)\nscene.relate.is_altitude(lineBC, triangleABC, B)\nscene.relate.point_lies_on(E, arcDEG)\n\n### Extra relationships\n\nscene.constraint.eq(lineAB.length, lineDG.length)\nscene.constraint.leq(arcDEG.central_angle, 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "right_triangle(A, B, C)", "arcDEG": "minor_arc(D, E, G)", "lineAB": "line_segment(A, B)", "lineBC": "line_segment(B, C)", "lineAC": "line_segment(A, C)", "lineDG": "line_segment(D, G)"}, "Rels": ["parallel(lineAB, lineDG)", "is_altitude(lineBC, triangleABC, B)", "point_lies_on(E, arcDEG)"], "Points": ["A", "B", "C", "D", "E", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('lineAB').length, scene.get_object('lineDG').length)", "scene.constraint.leq(scene.get_object('arcDEG').central_angle, 90)"], "possible_solution": {"points": {"A": [-7.562727284403612, 9.166395492611601], "B": [7.954873053223871, -3.388115013232786], "C": [8.081294484773032, -3.231848094693455], "D": [9.55379166392985, -7.0709734353118945], "E": [-8.913401782139408, 0.5036189075784779], "G": [-5.963809146883595, 5.483537637138205]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0174", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a major arc BC. There is a line segment BC. There is a line segment AD. The angle DAC is obtuse. Line BC is a chord of the circle. Point D lies on the circle. Further, the central angle of the major arc equals twice the inscribed angle that subtends the same arc.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\nmajor_arc1 = scene.add.major_arc(A, B, C)\nline_BC = scene.add.line_segment(B, C)\nline_AD = scene.add.line_segment(A, D)\n\n### relationships\n\nscene.relate.obtuse_angle(D, A, C)\nscene.relate.is_chord(line_BC, circle1)\nscene.relate.point_lies_on(D, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(major_arc1.central_angle, 2 * major_arc1.inscribed_angle)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "major_arc1": "major_arc(A, B, C)", "line_BC": "line_segment(B, C)", "line_AD": "line_segment(A, D)"}, "Rels": ["obtuse_angle(D, A, C)", "is_chord(line_BC, circle1)", "point_lies_on(D, circle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('major_arc1').central_angle, 2 * scene.get_object('major_arc1').inscribed_angle)"], "possible_solution": {"points": {"A": [2.7886142477293374, 2.2207901379148596], "B": [2.500437619901654, 3.4385976437504477], "C": [4.004366675316896, 2.5175171490141657], "D": [2.307792461471651, 3.3761737488959875]}, "circles": {"A": 1.2514395233125741}}}
{"unique_id": "2obj_3rel_1extra_gen0176", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is an isosceles triangle BCD. There is a line segment BC. There is a line segment CD. There is a line segment BD. Point B lies on the circle. Point C lies on the circle. Line BC is a chord of the circle. Further, the area of triangle BCD is equal to one-fourth the area of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.isosceles_triangle(B, C, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_BD = scene.add.line_segment(B, D)\n\n### relationships\n\nscene.relate.point_lies_on(B, circle1)\nscene.relate.point_lies_on(C, circle1)\nscene.relate.is_chord(line_BC, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.area, circle1.area / 4)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "isosceles_triangle(B, C, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_BD": "line_segment(B, D)"}, "Rels": ["point_lies_on(B, circle1)", "point_lies_on(C, circle1)", "is_chord(line_BC, circle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('circle1').area / 4)"], "possible_solution": {"points": {"A": [0.3563510003402143, -2.960817837793323], "B": [0.7228540181605793, -1.2823734211324769], "C": [-1.2502836419195007, -2.3523564488374875], "D": [-1.462628129213318, -0.11784403706327547]}, "circles": {"A": 1.7179930526828386}}}
{"unique_id": "2obj_3rel_1extra_gen0177", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a rectangle with points A, B, C, D. There is a minor arc with center E, start point F, and end point G. There is a line segment AB. There is a line segment BC. There is a line segment CD. There is a line segment DA. There is a line segment EF. There is a line segment EG. Line AB is parallel to line CD. Line AB is perpendicular to line BC. Point F lies on the minor arc. Further, the length of line EF equals the length of line AB and the angle FEG measures 60 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\narc1 = scene.add.minor_arc(E, F, G)\nline_AB = scene.add.line_segment(A, B)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_DA = scene.add.line_segment(D, A)\nline_EF = scene.add.line_segment(E, F)\nline_EG = scene.add.line_segment(E, G)\n\n### relationships\n\nscene.relate.parallel(line_AB, line_CD)\nscene.relate.perpendicular(line_AB, line_BC)\nscene.relate.point_lies_on(F, arc1)\n\n### Extra relationships\n\nscene.constraint.eq(line_EF.length, line_AB.length)\nscene.constraint.eq(scene.angle(scene.get_object('E'), scene.get_object('F'), scene.get_object('G')), 60)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "arc1": "minor_arc(E, F, G)", "line_AB": "line_segment(A, B)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_DA": "line_segment(D, A)", "line_EF": "line_segment(E, F)", "line_EG": "line_segment(E, G)"}, "Rels": ["parallel(line_AB, line_CD)", "perpendicular(line_AB, line_BC)", "point_lies_on(F, arc1)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_EF').length, scene.get_object('line_AB').length)", "scene.constraint.eq(scene.angle(scene.get_object('E'), scene.get_object('F'), scene.get_object('G')), 60)"], "possible_solution": {"points": {"A": [0.5422684601274694, -5.310222587034916], "B": [-0.7394702213545471, 1.3324002928411594], "C": [2.696950659727222, 1.995480771858343], "D": [3.978689338525616, -4.64714210394196], "E": [-0.6537976389903255, -2.763388850079376], "F": [-0.7443346055589688, 4.001158011221854], "G": [5.159203301009558, 0.6972919011830034]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0179", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is an equilateral triangle with vertices B, C, D. There are line segments BC, CD, DB, AD, AC, AB. The circle with center A is the circumcircle of triangle BCD. Line AB is a radius of the circle with center A. Line AC is a radius of the circle with center A. Line AD is a radius of the circle with center A.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.equilateral_triangle(B, C, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_DB = scene.add.line_segment(D, B)\nline_AD = scene.add.line_segment(A, D)\nline_AC = scene.add.line_segment(A, C)\nline_AB = scene.add.line_segment(A, B)\n\n### relationships\n\nscene.relate.is_circumcircle(circle1, triangle1)\nscene.relate.is_radius(line_AB, circle1)\nscene.relate.is_radius(line_AC, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "equilateral_triangle(B, C, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_DB": "line_segment(D, B)", "line_AD": "line_segment(A, D)", "line_AC": "line_segment(A, C)", "line_AB": "line_segment(A, B)"}, "Rels": ["is_circumcircle(circle1, triangle1)", "is_radius(line_AB, circle1)", "is_radius(line_AC, circle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": [], "possible_solution": {"points": {"A": [-1.2544281271965845, -0.7957544587334185], "B": [-1.727439183969253, -0.6829658690416003], "C": [-0.9202448079784407, -0.4425091868221735], "D": [-1.115600380218042, -1.2617883576727242]}, "circles": {"A": 0.4862722607842864}}}
{"unique_id": "2obj_3rel_1extra_gen0182", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a scalene triangle BCD. There are line segments BC, CD, DB, AD, AC, AB. Point A is the centroid of triangle BCD. The circle is the circumcircle of triangle BCD. Line AB is a radius of the circle. Further, the area of triangle BCD is one-fourth the area of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.scalene_triangle(B, C, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_DB = scene.add.line_segment(D, B)\nline_AD = scene.add.line_segment(A, D)\nline_AC = scene.add.line_segment(A, C)\nline_AB = scene.add.line_segment(A, B)\n\n### relationships\n\nscene.relate.is_centroid(A, triangle1)\nscene.relate.is_circumcircle(circle1, triangle1)\nscene.relate.is_radius(line_AB, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.area, circle1.area / 4)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "scalene_triangle(B, C, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_DB": "line_segment(D, B)", "line_AD": "line_segment(A, D)", "line_AC": "line_segment(A, C)", "line_AB": "line_segment(A, B)"}, "Rels": ["is_centroid(A, triangle1)", "is_circumcircle(circle1, triangle1)", "is_radius(line_AB, circle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('circle1').area / 4)"], "possible_solution": {"points": {"A": [0.4909462412168855, -2.780235196348583], "B": [0.5309000715864519, -2.589977205831686], "C": [0.30721224932925784, -2.8407331779090175], "D": [0.6343919363915426, -2.9101980814117203]}, "circles": {"A": 0.19870227550810352}}}
{"unique_id": "2obj_3rel_1extra_gen0198", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a semicircle with center A, start point B, and end point C. There is a circle with center D. There is a line segment AB. There is a line segment AC. There is a line segment BC. There is a line segment AD. There is a line segment BD. Point A lies on the circle. Point B lies on the circle. Line AB is a diameter of the circle. Further, length of line AD is equal to length of line BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\nsemicircle1 = scene.add.major_arc(A, B, C)\ncircle1 = scene.add.circle(D)\nline_AB = scene.add.line_segment(A, B)\nline_AC = scene.add.line_segment(A, C)\nline_BC = scene.add.line_segment(B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BD = scene.add.line_segment(B, D)\n\n### relationships\n\nscene.relate.point_lies_on(A, circle1)\nscene.relate.point_lies_on(B, circle1)\nscene.relate.is_diameter(line_AB, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BD.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"semicircle1": "major_arc(A, B, C)", "circle1": "circle(D)", "line_AB": "line_segment(A, B)", "line_AC": "line_segment(A, C)", "line_BC": "line_segment(B, C)", "line_AD": "line_segment(A, D)", "line_BD": "line_segment(B, D)"}, "Rels": ["point_lies_on(A, circle1)", "point_lies_on(B, circle1)", "is_diameter(line_AB, circle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BD').length)"], "possible_solution": {"points": {"A": [0.10300697762616869, -0.7122115696442107], "B": [-0.895637007004744, -1.4479136369042636], "C": [-0.7625641213770051, -1.6006562864782985], "D": [-0.3963150162735482, -1.0800626061973417]}, "circles": {"D": 0.6201909622030682}}}
{"unique_id": "2obj_3rel_1extra_gen0202", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a rectangle with corners A, B, C, D. There is a minor arc with center E, start point F, and end point G. There is a line segment AB. There is a line segment BC. There is a line segment CD. There is a line segment DA. There is a line segment EF. There is a line segment EG. Line AB is rotated around point B by 90 degrees to form line BC. Line AB is perpendicular to line BC. Point F lies on the minor arc with center E, start point F, and end point G. Further, the central angle of the minor arc with center E, start point F, and end point G is 90 degrees, and the length of line AB is less than or equal to the length of line BC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\nminor_arc1 = scene.add.minor_arc(E, F, G)\nline_AB = scene.add.line_segment(A, B)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_DA = scene.add.line_segment(D, A)\nline_EF = scene.add.line_segment(E, F)\nline_EG = scene.add.line_segment(E, G)\n\n### relationships\n\nscene.relate.rotation_around_point(line_AB, line_BC, B, 90)\nscene.relate.perpendicular(line_AB, line_BC)\nscene.relate.point_lies_on(F, minor_arc1)\n\n### Extra relationships\n\nscene.constraint.eq(minor_arc1.central_angle, 90)\nscene.constraint.leq(line_AB.length, line_BC.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "minor_arc1": "minor_arc(E, F, G)", "line_AB": "line_segment(A, B)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_DA": "line_segment(D, A)", "line_EF": "line_segment(E, F)", "line_EG": "line_segment(E, G)"}, "Rels": ["rotation_around_point(line_AB, line_BC, B, 90)", "perpendicular(line_AB, line_BC)", "point_lies_on(F, minor_arc1)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('minor_arc1').central_angle, 90)", "scene.constraint.leq(scene.get_object('line_AB').length, scene.get_object('line_BC').length)"], "possible_solution": {"points": {"A": [2.138239514613247, 3.759959818056236], "B": [1.8186946220177238, 3.1664805623587124], "C": [2.412173960103176, 2.8469356885832116], "D": [2.7317187542459997, 3.4404149856425557], "E": [-1.5552294469329313, -0.6099314999158587], "F": [-0.3177639177574062, 3.1255358975033087], "G": [2.1802379606352074, -1.8473970299861127]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0221", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a major arc with center A and endpoints B and C. There is a semicircle with center D and endpoints E and F. There is a line segment BE. There is a line segment CF. There is a line segment AD. Line segment BE intersects line segment CF at G. Point G lies on the major arc with center A and endpoints B and C. Line segment AD is perpendicular to line segment BE.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\nmajor_arc1 = scene.add.major_arc(A, B, C)\nsemicircle1 = scene.add.semicircle(D, E, F)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_AD = scene.add.line_segment(A, D)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_BE, line_CF, G)\nscene.relate.point_lies_on(G, major_arc1)\nscene.relate.perpendicular(line_AD, line_BE)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"major_arc1": "major_arc(A, B, C)", "semicircle1": "semicircle(D, E, F)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_AD": "line_segment(A, D)"}, "Rels": ["lines_intersect_at(line_BE, line_CF, G)", "point_lies_on(G, major_arc1)", "perpendicular(line_AD, line_BE)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [0.7438486180233891, 2.3349107442676496], "B": [0.8705829962383682, 1.6610366431320356], "C": [0.4626316971667415, 1.7095422391254442], "D": [0.7837426165084537, 1.2447352766558928], "E": [-1.7573510960269483, 1.564869841567684], "F": [3.324836278601968, 0.9246008094578967], "G": [0.6667066684520047, 1.6535759952944495]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0224", "nl_description": "Diagram description: The diagram contains points A, B, C, O, D, E, F. There is a triangle with vertices A, B, C. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is a median of triangle ABC from vertex A. The circle with center O is the circumcircle of triangle ABC. Line AD is perpendicular to line BE.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"O\", \"D\", \"E\", \"F\"])\n\ntriangle_ABC = scene.add.triangle(A, B, C)\ncircle_O = scene.add.circle(O)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_median(line_AD, triangle_ABC, A)\nscene.relate.is_circumcircle(circle_O, triangle_ABC)\nscene.relate.perpendicular(line_AD, line_BE)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle_ABC": "triangle(A, B, C)", "circle_O": "circle(O)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["is_median(line_AD, triangle_ABC, A)", "is_circumcircle(circle_O, triangle_ABC)", "perpendicular(line_AD, line_BE)"], "Points": ["A", "B", "C", "O", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [6.808852523047716, 8.814579401894346], "B": [-6.079908892349075, 2.626118811101104], "C": [0.3711986756888032, -6.39703284987886], "O": [2.2605228279558442, 1.7714276814450018], "D": [-2.8543555387375297, -1.8854568947299275], "E": [6.12766667654901, -8.398548711194897], "F": [-6.361928824022242, 8.401319673196502]}, "circles": {"O": 8.384109498055006}}}
{"unique_id": "2obj_3rel_1extra_gen0225", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a equilateral triangle with vertices A, B, C. There is a right triangle with vertices D, E, F. There is a line segment AC. There is a line segment DF. There is a line segment BE. The line AC is parallel to line DF. The line BE is perpendicular to line AC. Line BE is an altitude of triangle ABC from vertex B.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ntriangle1 = scene.add.equilateral_triangle(A, B, C)\ntriangle2 = scene.add.right_triangle(D, E, F)\nline_AC = scene.add.line_segment(A, C)\nline_DF = scene.add.line_segment(D, F)\nline_BE = scene.add.line_segment(B, E)\n\n### relationships\n\nscene.relate.parallel(line_AC, line_DF)\nscene.relate.perpendicular(line_BE, line_AC)\nscene.relate.is_altitude(line_BE, triangle1, B)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "equilateral_triangle(A, B, C)", "triangle2": "right_triangle(D, E, F)", "line_AC": "line_segment(A, C)", "line_DF": "line_segment(D, F)", "line_BE": "line_segment(B, E)"}, "Rels": ["parallel(line_AC, line_DF)", "perpendicular(line_BE, line_AC)", "is_altitude(line_BE, triangle1, B)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.2989274905333746, 4.908214262170263], "B": [4.721852847153345, 4.6109833206455555], "C": [1.9540531226632047, 0.41147556941229774], "D": [1.5073409711436454, 3.9354969549424217], "E": [0.8275628386027207, 2.659844841627244], "F": [2.626872596243438, 1.7010164881249223]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0231", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is an isosceles trapezoid ABCD. There is a major arc FG with center E. There is a line segment AD. There is a line segment BC. There is a line segment EF. There is a line segment EG. Point F lies on the major arc FG. Point G lies on the major arc FG. The isosceles trapezoid ABCD is mirrored across line EF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntrapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)\narc1 = scene.add.major_arc(E, F, G)\nline_AD = scene.add.line_segment(A, D)\nline_BC = scene.add.line_segment(B, C)\nline_EF = scene.add.line_segment(E, F)\nline_EG = scene.add.line_segment(E, G)\n\n### relationships\n\nscene.relate.point_lies_on(F, arc1)\nscene.relate.point_lies_on(G, arc1)\nscene.relate.mirror_across_line(trapezoid1, trapezoid1, line_EF)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "isosceles_trapezoid(A, B, C, D)", "arc1": "major_arc(E, F, G)", "line_AD": "line_segment(A, D)", "line_BC": "line_segment(B, C)", "line_EF": "line_segment(E, F)", "line_EG": "line_segment(E, G)"}, "Rels": ["point_lies_on(F, arc1)", "point_lies_on(G, arc1)", "mirror_across_line(trapezoid1, trapezoid1, line_EF)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [-9.72300169928753, -9.17061441834715], "B": [4.461183750448578, 9.633538501330733], "C": [4.581724622026659, 9.796119672638113], "D": [-9.846219286982414, -9.331187377693732], "E": [-8.778803655670014, -7.917486573777599], "F": [2.4849937039862597, 7.015066693213747], "G": [9.809300915632386, -9.999944438302164]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0233", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a major arc with center A and endpoints B and C. There is a parallelogram with vertices D, E, F, G. There is a line segment DH. There is a line segment GI. There is a line segment EF. The angle BAC is a right angle. Line DH is perpendicular to line EF. Point H lies on the major arc BC. Further, the central angle of the major arc equals twice its inscribed angle, and the length of line DH is less than or equal to the radius of the major arc.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\nmajor_arc1 = scene.add.major_arc(A, B, C)\nparallelogram1 = scene.add.parallelogram(D, E, F, G)\nline_DH = scene.add.line_segment(D, H)\nline_GI = scene.add.line_segment(G, I)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.right_angle(B, A, C)\nscene.relate.perpendicular(line_DH, line_EF)\nscene.relate.point_lies_on(H, major_arc1)\n\n### Extra relationships\n\nscene.constraint.eq(major_arc1.central_angle, 2 * major_arc1.inscribed_angle)\nscene.constraint.leq(line_DH.length, major_arc1.radius)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"major_arc1": "major_arc(A, B, C)", "parallelogram1": "parallelogram(D, E, F, G)", "line_DH": "line_segment(D, H)", "line_GI": "line_segment(G, I)", "line_EF": "line_segment(E, F)"}, "Rels": ["right_angle(B, A, C)", "perpendicular(line_DH, line_EF)", "point_lies_on(H, major_arc1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": ["scene.constraint.eq(scene.get_object('major_arc1').central_angle, 2 * scene.get_object('major_arc1').inscribed_angle)", "scene.constraint.leq(scene.get_object('line_DH').length, scene.get_object('major_arc1').radius)"], "possible_solution": {"points": {"A": [1.3882454061843796, 2.013163252197613], "B": [0.6635299400972043, 2.134648436226026], "C": [1.2667602116199423, 1.2884477578041968], "D": [1.3705773094884317, 2.661850402100078], "E": [3.9368109781694707, 0.5500006155830727], "F": [2.6675204527293475, -2.23806858568845], "G": [0.10128677221440427, -0.12621881781112695], "H": [2.0368589318744985, 2.3585204340770454], "I": [9.837949979113542, 3.8693526353017056]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0242", "nl_description": "Diagram description: The diagram contains points A, B, C, O, D, E, F. There is an acute triangle ABC. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. O is the orthocenter of triangle ABC. line AD is an altitude of triangle ABC from vertex A. line BE is an altitude of triangle ABC from vertex B. Further, the length of line AD is equal to the length of line BE, and the area of triangle ABC is less than or equal to 10.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"O\", \"D\", \"E\", \"F\"])\n\ntriangle_ABC = scene.add.acute_triangle(A, B, C)\ncircle_O = scene.add.circle(O)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_orthocenter(O, triangle_ABC)\nscene.relate.is_altitude(line_AD, triangle_ABC, A)\nscene.relate.is_altitude(line_BE, triangle_ABC, B)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BE.length)\nscene.constraint.leq(triangle_ABC.area, 10)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle_ABC": "acute_triangle(A, B, C)", "circle_O": "circle(O)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["is_orthocenter(O, triangle_ABC)", "is_altitude(line_AD, triangle_ABC, A)", "is_altitude(line_BE, triangle_ABC, B)"], "Points": ["A", "B", "C", "O", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)", "scene.constraint.leq(scene.get_object('triangle_ABC').area, 10)"], "possible_solution": {"points": {"A": [0.22150986735847406, -3.906226443919282], "B": [0.9096302929098395, -0.41373167529350635], "C": [5.854601257196282, -3.2020681504740036], "O": [1.1421179319783392, -2.273575379850908], "D": [1.8817466842422217, -0.9618820640409035], "E": [1.3289017098665796, -3.7677981160320746], "F": [9.690303449349214, -2.5502119903214404]}, "circles": {"O": 4.491322488431648}}}
{"unique_id": "2obj_3rel_1extra_gen0248", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a parallelogram ABCD. There is a rectangle EFGH. There is a line segment AC. There is a line segment EG. There is a line segment AB. There is a line segment EF. Parallelogram ABCD is scaled by a factor of 2 to form rectangle EFGH. Line AC is perpendicular to line EG. Line AB is parallel to line EF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\nparallelogram1 = scene.add.parallelogram(A, B, C, D)\nrectangle1 = scene.add.rectangle(E, F, G, H)\nline_AC = scene.add.line_segment(A, C)\nline_EG = scene.add.line_segment(E, G)\nline_AB = scene.add.line_segment(A, B)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.scale(parallelogram1, rectangle1, 2)\nscene.relate.perpendicular(line_AC, line_EG)\nscene.relate.parallel(line_AB, line_EF)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"parallelogram1": "parallelogram(A, B, C, D)", "rectangle1": "rectangle(E, F, G, H)", "line_AC": "line_segment(A, C)", "line_EG": "line_segment(E, G)", "line_AB": "line_segment(A, B)", "line_EF": "line_segment(E, F)"}, "Rels": ["scale(parallelogram1, rectangle1, 2)", "perpendicular(line_AC, line_EG)", "parallel(line_AB, line_EF)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [4.045711437946783, 3.3545360008705942], "B": [3.373248522527794, -1.2981450450526486], "C": [0.6853215893927947, 1.3662165138478832], "D": [1.357784523351778, 6.018897598375682], "E": [2.023468731869455, -1.44687051066424], "F": [2.3597001858331375, 0.8794701700153392], "G": [0.4868228389713347, 1.150161464765277], "H": [0.15059140364685777, -1.1761790843769622]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0251", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is an equilateral triangle BCD. There is a line segment BC. There is a line segment CD. There is a line segment DB. Point B lies on the circle. Point C lies on the circle. The circle is the circumcircle of triangle BCD. Further, the perimeter of triangle BCD equals three times the length of line BC. Further, the length of line BC equals the length of line CD. Further, the length of line CD equals the length of line DB.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.equilateral_triangle(B, C, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_DB = scene.add.line_segment(D, B)\n\n### relationships\n\nscene.relate.point_lies_on(B, circle1)\nscene.relate.point_lies_on(C, circle1)\nscene.relate.is_circumcircle(circle1, triangle1)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.perimeter, 3 * line_BC.length)\nscene.constraint.eq(line_BC.length, line_CD.length)\nscene.constraint.eq(line_CD.length, line_DB.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "equilateral_triangle(B, C, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_DB": "line_segment(D, B)"}, "Rels": ["point_lies_on(B, circle1)", "point_lies_on(C, circle1)", "is_circumcircle(circle1, triangle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').perimeter, 3 * scene.get_object('line_BC').length)", "scene.constraint.eq(scene.get_object('line_BC').length, scene.get_object('line_CD').length)", "scene.constraint.eq(scene.get_object('line_CD').length, scene.get_object('line_DB').length)"], "possible_solution": {"points": {"A": [2.5774006610224562, -2.7346801910119916], "B": [1.810053569408442, -3.6091901196068656], "C": [3.718422015180598, -2.961967288387693], "D": [2.203726383533423, -1.6328831475138132]}, "circles": {"A": 1.1634385079009606}}}
{"unique_id": "2obj_3rel_1extra_gen0267", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a circle with center E. There is a rhombus with vertices A, B, C, D. There is a line segment AC. There is a line segment BD. Line AC is perpendicular to line BD. Line AC is a diameter of the circle. Further, the area of rhombus ABCD equals the area of circle E.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nrhombus1 = scene.add.rhombus(A, B, C, D)\ncircle1 = scene.add.circle(E)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\n\n### relationships\n\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.perpendicular(line_AC, line_BD)\n\n### Extra relationships\n\nscene.constraint.eq(rhombus1.area, circle1.area)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rhombus1": "rhombus(A, B, C, D)", "circle1": "circle(E)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)"}, "Rels": ["is_diameter(line_AC, circle1)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('rhombus1').area, scene.get_object('circle1').area)"], "possible_solution": {"points": {"A": [-0.23521497185986978, -1.0913749303070623], "B": [-1.0197515744273533, 0.2865609387755155], "C": [0.5607241198578431, 0.4142385533936263], "D": [1.3452607480361043, -0.963697325719206], "E": [0.16275466832778435, -0.33856821983154606]}, "circles": {"E": 0.8515267588357309}}}
{"unique_id": "2obj_3rel_1extra_gen0273", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a minor arc BC with center A. There is a major arc DE with center A. There is a line segment BD. There is a line segment CE. There is a line segment DE. Point B lies on minor arc BC. Point D lies on major arc DE. Line BD is perpendicular to line CE.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nminor_arc1 = scene.add.minor_arc(A, B, C)\nmajor_arc2 = scene.add.major_arc(A, D, E)\nline_BD = scene.add.line_segment(B, D)\nline_CE = scene.add.line_segment(C, E)\nline_DE = scene.add.line_segment(D, E)\n\n### relationships\n\nscene.relate.point_lies_on(B, minor_arc1)\nscene.relate.point_lies_on(D, major_arc2)\nscene.relate.perpendicular(line_BD, line_CE)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"minor_arc1": "minor_arc(A, B, C)", "major_arc2": "major_arc(A, D, E)", "line_BD": "line_segment(B, D)", "line_CE": "line_segment(C, E)", "line_DE": "line_segment(D, E)"}, "Rels": ["point_lies_on(B, minor_arc1)", "point_lies_on(D, major_arc2)", "perpendicular(line_BD, line_CE)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [0.29361295866281134, 0.1492264692390311], "B": [-0.8949923043203999, -4.04668648157488], "C": [4.348045429426287, -1.4570254723147777], "D": [0.4061738413084981, -2.3982811392619285], "E": [-0.6751550551797054, 2.5080298748971934]}, "circles": {}}}
{"unique_id": "2obj_3rel_1extra_gen0284", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a minor arc with center A, start point B, and end point C. There is a regular octagon with vertices D, E, F, G, H, I, J, K. There is a line segment AB. There is a line segment AC. There is a line segment DE. There is a line segment EF. Point B lies on the minor arc. Point C lies on the minor arc. Line AB is perpendicular to line AC. Further, the inscribed angle of the minor arc is 45 degrees. Further, the area of the regular octagon is less than or equal to 20 square units.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\"])\n\nminor_arc1 = scene.add.minor_arc(A, B, C)\nregular_octagon1 = scene.add.regular_octagon(D, E, F, G, H, I, J, K)\nline_AB = scene.add.line_segment(A, B)\nline_AC = scene.add.line_segment(A, C)\nline_DE = scene.add.line_segment(D, E)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.point_lies_on(B, minor_arc1)\nscene.relate.point_lies_on(C, minor_arc1)\nscene.relate.perpendicular(line_AB, line_AC)\n\n### Extra relationships\n\nscene.constraint.eq(minor_arc1.inscribed_angle, 45)\nscene.constraint.leq(regular_octagon1.area, 20)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"minor_arc1": "minor_arc(A, B, C)", "regular_octagon1": "regular_octagon(D, E, F, G, H, I, J, K)", "line_AB": "line_segment(A, B)", "line_AC": "line_segment(A, C)", "line_DE": "line_segment(D, E)", "line_EF": "line_segment(E, F)"}, "Rels": ["point_lies_on(B, minor_arc1)", "point_lies_on(C, minor_arc1)", "perpendicular(line_AB, line_AC)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K"], "extra_rel": ["scene.constraint.eq(scene.get_object('minor_arc1').inscribed_angle, 45)", "scene.constraint.leq(scene.get_object('regular_octagon1').area, 20)"], "possible_solution": {"points": {"A": [-10.0, -10.0], "B": [-10.0, 10.0], "C": [10.0, -10.0], "D": [4.9202872722613336, 0.10082159333948573], "E": [4.721341109528313, 0.20939363003827427], "F": [4.503892905371804, 0.14548947267566092], "G": [4.395320868673015, -0.05345669005735985], "H": [4.459225026035629, -0.2709048942138693], "I": [4.658171188768649, -0.3794769309126579], "J": [4.875619392925159, -0.31557277355004454], "K": [4.984191429623947, -0.11662661081702377]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0005", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a major arc with center A, start point B, end point C. There is a circle with center D. There is a line segment AC. There is a line segment BC. There is a line segment AD. There is a line segment BD. There is a line segment CD. Line AC and line BC intersect at C. Line CD is the angle bisector of angle ACB. Line AD is a radius of the circle. Line BD is a radius of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\nsemicircle1 = scene.add.major_arc(A, B, C)\ncircle1 = scene.add.circle(D)\nline_AC = scene.add.line_segment(A, C)\nline_BC = scene.add.line_segment(B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BD = scene.add.line_segment(B, D)\nline_CD = scene.add.line_segment(C, D)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_BC, C)\nscene.relate.angle_bisector(A, C, B, line_CD)\nscene.relate.is_radius(line_AD, circle1)\nscene.relate.is_radius(line_BD, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"semicircle1": "major_arc(A, B, C)", "circle1": "circle(D)", "line_AC": "line_segment(A, C)", "line_BC": "line_segment(B, C)", "line_AD": "line_segment(A, D)", "line_BD": "line_segment(B, D)", "line_CD": "line_segment(C, D)"}, "Rels": ["lines_intersect_at(line_AC, line_BC, C)", "angle_bisector(A, C, B, line_CD)", "is_radius(line_AD, circle1)", "is_radius(line_BD, circle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": [], "possible_solution": {"points": {"A": [-2.5529065904146804, -0.162904093739504], "B": [3.4496802282188415, 1.7857036009829674], "C": [1.6921651676590983, -4.8327527220346935], "D": [-0.08219874172685579, 2.445841559702657]}, "circles": {"D": 3.593042045094468}}}
{"unique_id": "2obj_4rel_2extra_gen0009", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a square with vertices A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment EA. There is a line segment AB. E is the centroid of the square. Points A, E, and C are collinear. Line segment AC is a diameter of the circle. Line segment EA is a radius of the circle. Further, the area of the circle equals the area of the square. Further, angle AEB is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nsquare1 = scene.add.square(A, B, C, D)\ncircle1 = scene.add.circle(E)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EA = scene.add.line_segment(E, A)\nline_AB = scene.add.line_segment(A, B)\n\n### relationships\n\nscene.relate.is_centroid(E, square1)\nscene.relate.collinear(A, E, C)\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.is_radius(line_EA, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(circle1.area, square1.area)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('E'), scene.get_object('B')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"square1": "square(A, B, C, D)", "circle1": "circle(E)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EA": "line_segment(E, A)", "line_AB": "line_segment(A, B)"}, "Rels": ["is_centroid(E, square1)", "collinear(A, E, C)", "is_diameter(line_AC, circle1)", "is_radius(line_EA, circle1)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('circle1').area, scene.get_object('square1').area)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('E'), scene.get_object('B')), 90)"], "possible_solution": {"points": {"A": [-2.1756376401975275, 1.0465165025170673], "B": [-2.0307932499703423, 1.2829226853759923], "C": [-1.801718485841509, 1.1285127540904718], "D": [-1.9468086523157015, 0.8945241680221326], "E": [-1.988966275455871, 1.0862080195266308]}, "circles": {"E": 0.16515842019975116}}}
{"unique_id": "2obj_4rel_2extra_gen0010", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a major arc with center B and endpoints C and D. There are line segments AB, AC, AD, BC, and CD. Point B lies on the circle. Point C lies on the circle. Point D lies on the circle. Line AB intersects line CD at point A.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\nsemicircle1 = scene.add.major_arc(B, C, D)\nline_AB = scene.add.line_segment(A, B)\nline_AC = scene.add.line_segment(A, C)\nline_AD = scene.add.line_segment(A, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\n\n### relationships\n\nscene.relate.point_lies_on(B, circle1)\nscene.relate.point_lies_on(C, circle1)\nscene.relate.point_lies_on(D, circle1)\nscene.relate.lines_intersect_at(line_AB, line_CD, A)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "semicircle1": "major_arc(B, C, D)", "line_AB": "line_segment(A, B)", "line_AC": "line_segment(A, C)", "line_AD": "line_segment(A, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)"}, "Rels": ["point_lies_on(B, circle1)", "point_lies_on(C, circle1)", "point_lies_on(D, circle1)", "lines_intersect_at(line_AB, line_CD, A)"], "Points": ["A", "B", "C", "D"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.3744262949582405, -0.2800487264314149], "B": [0.28562725485706186, -0.6963409640752234], "C": [0.041865937653721444, 0.38000481864673674], "D": [-0.7907185279023172, -0.9401022664105054]}, "circles": {"A": 0.7803652417300825}}}
{"unique_id": "2obj_4rel_2extra_gen0012", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a circle with center A. There is a kite BCDE. There is a line segment BC. There is a line segment CD. There is a line segment DE. There is a line segment BE. There is a line segment AC. There is a line segment AD. B, A, and C are collinear. The angle at A formed by points B and D is a right angle. Line segment AC is a radius of the circle. Line segment AD is a radius of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ncircle1 = scene.add.circle(A)\nkite1 = scene.add.kite(B, C, D, E)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_DE = scene.add.line_segment(D, E)\nline_BE = scene.add.line_segment(B, E)\nline_AC = scene.add.line_segment(A, C)\nline_AD = scene.add.line_segment(A, D)\n\n### relationships\n\nscene.relate.collinear(B, A, C)\nscene.relate.right_angle(B, A, D)\nscene.relate.is_radius(line_AC, circle1)\nscene.relate.is_radius(line_AD, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "kite1": "kite(B, C, D, E)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_DE": "line_segment(D, E)", "line_BE": "line_segment(B, E)", "line_AC": "line_segment(A, C)", "line_AD": "line_segment(A, D)"}, "Rels": ["collinear(B, A, C)", "right_angle(B, A, D)", "is_radius(line_AC, circle1)", "is_radius(line_AD, circle1)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.9139620274393017, 1.219964209144901], "B": [-1.2087986442277066, 1.353467241817099], "C": [-0.20216395496026324, 0.8976597048856833], "D": [-0.5916576843031168, 1.9317623852582018], "E": [9.999892867750384, -9.989701518513485]}, "circles": {"A": 0.7813684792631549}}}
{"unique_id": "2obj_4rel_2extra_gen0024", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a trapezoid ABCD. There is a scalene triangle EFG. There are line segments AC, BD, EF, FG, GE. Line AC and line BD intersect at point H. Line AC is perpendicular to line BD. Point H is the centroid of trapezoid ABCD. Line EF is an altitude of triangle EFG from vertex E. Further, length of line AC is equal to length of line BD, and angle AHB is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntrapezoid1 = scene.add.trapezoid(A, B, C, D)\ntriangle1 = scene.add.scalene_triangle(E, F, G)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\nline_FG = scene.add.line_segment(F, G)\nline_GE = scene.add.line_segment(G, E)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_BD, H)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.is_centroid(H, trapezoid1)\nscene.relate.is_altitude(line_EF, triangle1, E)\n\n### Extra relationships\n\nscene.constraint.eq(line_BD.length, line_AC.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('H'), scene.get_object('B')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "trapezoid(A, B, C, D)", "triangle1": "scalene_triangle(E, F, G)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)", "line_FG": "line_segment(F, G)", "line_GE": "line_segment(G, E)"}, "Rels": ["lines_intersect_at(line_AC, line_BD, H)", "perpendicular(line_AC, line_BD)", "is_centroid(H, trapezoid1)", "is_altitude(line_EF, triangle1, E)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_BD').length, scene.get_object('line_AC').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('H'), scene.get_object('B')), 90)"], "possible_solution": {"points": {"A": [4.653905614665019, 2.5064071231042875], "B": [-0.6629254674025051, -1.6744266373839438], "C": [3.51790816952992, -6.991258209258448], "D": [8.834739774070215, -2.810424088564485], "E": [-2.321730654086869, -4.5355663373433535], "F": [-0.7349493314638589, -3.8695779042495135], "G": [-4.900684083926567, 6.055687523748188], "H": [4.085906942954608, -2.2424253099209484]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0030", "nl_description": "Diagram description: The diagram contains points A, B, C, O, D, E, F, G. There is an isosceles triangle ABC with AB = BC. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is parallel to line BE. Line AD intersects line CF at point G. Line AD is an altitude of triangle ABC from vertex A. The circle is the circumcircle of triangle ABC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"O\", \"D\", \"E\", \"F\", \"G\"])\n\ntriangleABC = scene.add.isosceles_triangle(A, B, C)\ncircleO = scene.add.circle(O)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.parallel(line_AD, line_BE)\nscene.relate.lines_intersect_at(line_AD, line_CF, G)\nscene.relate.is_altitude(line_AD, triangleABC, A)\nscene.relate.is_circumcircle(circleO, triangleABC)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "isosceles_triangle(A, B, C)", "circleO": "circle(O)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["parallel(line_AD, line_BE)", "lines_intersect_at(line_AD, line_CF, G)", "is_altitude(line_AD, triangleABC, A)", "is_circumcircle(circleO, triangleABC)"], "Points": ["A", "B", "C", "O", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [0.1173222810191722, 1.392290347079089], "B": [1.7128001797454278, -0.43964216269255313], "C": [-0.6365307646009134, 0.17855576747111568], "O": [0.6332377427112511, 0.23087669204797293], "D": [-0.23019294384122307, 0.07163280089452136], "E": [1.6232633184546348, -0.7799071379963247], "F": [0.3572178126000123, 1.391723420815365], "G": [0.003566975432487628, 0.9599866232348425]}, "circles": {"O": 1.2708456229942602}}}
{"unique_id": "2obj_4rel_2extra_gen0036", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a rhomboid ABCD. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment BC. Line AC intersects the circle at points A and C. Line BC is tangent to the circle at point C. Line AC is perpendicular to line BD. Line AC is a diameter of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nrhomboid1 = scene.add.rhomboid(A, B, C, D)\ncircle1 = scene.add.circle(E)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_BC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.line_intersects_circle_at(line_AC, circle1, A, C)\nscene.relate.tangent_to_circle(line_BC, circle1, C)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.is_diameter(line_AC, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rhomboid1": "rhomboid(A, B, C, D)", "circle1": "circle(E)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_BC": "line_segment(B, C)"}, "Rels": ["line_intersects_circle_at(line_AC, circle1, A, C)", "tangent_to_circle(line_BC, circle1, C)", "perpendicular(line_AC, line_BD)", "is_diameter(line_AC, circle1)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [0.24213202748408716, -2.3332283951441273], "B": [-1.3740401788036216, -7.211916350288757], "C": [0.6218008240772634, -2.4758929569205828], "D": [2.2379833914604763, 2.402791470507458], "E": [0.4342022116105775, -2.396992604706584]}, "circles": {"E": 0.20365721541465176}}}
{"unique_id": "2obj_4rel_2extra_gen0042", "nl_description": "Diagram description: The diagram contains points A, B, C, D, F. There is a circle with center A. There is a circle with center B. There is a line segment CD. There is a line segment AF. The circles are similar. Line AF is the angle bisector of angle CAD. Line CD is a chord of the circle with center A. Line CD is perpendicular to line AF. Further, the area of the circle with center A is equal to the area of the circle with center B and angle CAF is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"F\"])\n\ncircle1 = scene.add.circle(A)\ncircle2 = scene.add.circle(B)\nline_CD = scene.add.line_segment(C, D)\nline_AF = scene.add.line_segment(A, F)\n\n### relationships\n\nscene.relate.similar(circle1, circle2)\nscene.relate.angle_bisector(C, A, D, line_AF)\nscene.relate.is_chord(line_CD, circle1)\nscene.relate.perpendicular(line_CD, line_AF)\n\n### Extra relationships\n\nscene.constraint.eq(circle1.area, circle2.area)\nscene.constraint.eq(scene.angle(scene.get_object('C'), scene.get_object('A'), scene.get_object('F')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "circle2": "circle(B)", "line_CD": "line_segment(C, D)", "line_AF": "line_segment(A, F)"}, "Rels": ["similar(circle1, circle2)", "angle_bisector(C, A, D, line_AF)", "is_chord(line_CD, circle1)", "perpendicular(line_CD, line_AF)"], "Points": ["A", "B", "C", "D", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('circle1').area, scene.get_object('circle2').area)", "scene.constraint.eq(scene.angle(scene.get_object('C'), scene.get_object('A'), scene.get_object('F')), 90)"], "possible_solution": {"points": {"A": [0.6671048147929209, 1.894880809541353], "B": [8.302328988338873, -6.1883522764255545], "C": [2.7589443361026555, 3.8379269958830085], "D": [-1.4247346892167738, -0.04816537526082586], "F": [6.211835436285217, -4.0744505920888985]}, "circles": {"A": 2.855034325105019, "B": 2.855034324513472}}}
{"unique_id": "2obj_4rel_2extra_gen0053", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a right isosceles triangle BCD. There is a line segment BC. There is a line segment CD. There is a line segment BD. There is a line segment AD. There is a line segment AC. Line BC is tangent to the circle at point B. The angle at D in triangle BCD is obtuse. Line BD is a chord of the circle. Point D lies on the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.right_isosceles_triangle(B, C, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_BD = scene.add.line_segment(B, D)\nline_AD = scene.add.line_segment(A, D)\nline_AC = scene.add.line_segment(A, C)\n\n### relationships\n\nscene.relate.tangent_to_circle(line_BC, circle1, B)\nscene.relate.obtuse_angle(D, C, B)\nscene.relate.is_chord(line_BD, circle1)\nscene.relate.point_lies_on(D, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "right_isosceles_triangle(B, C, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_BD": "line_segment(B, D)", "line_AD": "line_segment(A, D)", "line_AC": "line_segment(A, C)"}, "Rels": ["tangent_to_circle(line_BC, circle1, B)", "obtuse_angle(D, C, B)", "is_chord(line_BD, circle1)", "point_lies_on(D, circle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.0034949857809214667, 1.4465584896758334], "B": [0.028230096261779747, 1.7280107779328422], "C": [0.3096293483345749, 1.6962915405687717], "D": [0.2779631072942547, 1.4148862732584877]}, "circles": {"A": 0.2832345454300741}}}
{"unique_id": "2obj_4rel_2extra_gen0054", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is an isosceles triangle ABC. There is a right triangle DEF. There are line segments AD, BE, CF, DE, AF, and BD. Angle ABC is acute. The extensions of line AD and line BE intersect at point G. Line AD is perpendicular to line BE. Line CF is an altitude of triangle ABC from vertex C. Further, the perimeters of triangle ABC and triangle DEF are equal, and angle ABC measures 75 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntriangle1 = scene.add.isosceles_triangle(A, B, C)\ntriangle2 = scene.add.right_triangle(D, E, F)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_DE = scene.add.line_segment(D, E)\nline_AF = scene.add.line_segment(A, F)\nline_BD = scene.add.line_segment(B, D)\n\n### relationships\n\nscene.relate.acute_angle(A, B, C)\nscene.relate.line_extensions_intersect_at(line_AD, line_BE, G)\nscene.relate.perpendicular(line_AD, line_BE)\nscene.relate.is_altitude(line_CF, triangle1, C)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.perimeter, triangle2.perimeter)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 75)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "isosceles_triangle(A, B, C)", "triangle2": "right_triangle(D, E, F)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_DE": "line_segment(D, E)", "line_AF": "line_segment(A, F)", "line_BD": "line_segment(B, D)"}, "Rels": ["acute_angle(A, B, C)", "line_extensions_intersect_at(line_AD, line_BE, G)", "perpendicular(line_AD, line_BE)", "is_altitude(line_CF, triangle1, C)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').perimeter, scene.get_object('triangle2').perimeter)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 75)"], "possible_solution": {"points": {"A": [2.5195653250426853, -3.826099870553639], "B": [1.233878474234381, -0.26360726848518984], "C": [-1.8744649645837335, -2.4275263804573064], "D": [-3.325403536547133, 1.1342943862800945], "E": [1.7945412509694476, 0.39703716479564466], "F": [1.5666392219287244, -1.185647550324933], "G": [0.014640182237065346, -1.7002688308047322]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0073", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a triangle with vertices B, C, D. There is a line segment BC. There is a line segment CD. There is a line segment BD. There is a line segment AD. There is a line segment AC. Line BC is perpendicular to line CD. Angle BCD is obtuse. Line BD is a chord of the circle. Line AD is a radius of the circle. Further, length of line CD is equal to length of line AD. Further, angle BCD is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.triangle(B, C, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_BD = scene.add.line_segment(B, D)\nline_AD = scene.add.line_segment(A, D)\nline_AC = scene.add.line_segment(A, C)\n\n### relationships\n\nscene.relate.perpendicular(line_BC, line_CD)\nscene.relate.obtuse_angle(B, C, D)\nscene.relate.is_chord(line_BD, circle1)\nscene.relate.is_radius(line_AD, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(line_CD.length, line_AD.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('C'), scene.get_object('D')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "triangle(B, C, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_BD": "line_segment(B, D)", "line_AD": "line_segment(A, D)", "line_AC": "line_segment(A, C)"}, "Rels": ["perpendicular(line_BC, line_CD)", "obtuse_angle(B, C, D)", "is_chord(line_BD, circle1)", "is_radius(line_AD, circle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_CD').length, scene.get_object('line_AD').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('C'), scene.get_object('D')), 90)"], "possible_solution": {"points": {"A": [0.7109213866184488, -0.8799265569654887], "B": [9.942967918727371, 0.08572586332820487], "C": [-0.9937981105214586, -1.2540667637048473], "D": [-2.1225082059698277, 7.959465067749211]}, "circles": {"A": 9.282411730403515}}}
{"unique_id": "2obj_4rel_2extra_gen0075", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is an isosceles trapezoid ABCD. There is a rectangle EFGH. There is a line segment AC. There is a line segment BD. There is a line segment EG. There is a line segment FH. Line AC and line BD intersect at point I. Line EG and line FH intersect at point J. Line AC is perpendicular to line BD. Line EG is perpendicular to line FH. Further, length of line AC is equal to length of line BD. Further, angle A I B is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\"])\n\ntrapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)\nrectangle1 = scene.add.rectangle(E, F, G, H)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EG = scene.add.line_segment(E, G)\nline_FH = scene.add.line_segment(F, H)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line_AC, line_BD, I)\nscene.relate.line_extensions_intersect_at(line_EG, line_FH, J)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.perpendicular(line_EG, line_FH)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('I'), scene.get_object('B')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "isosceles_trapezoid(A, B, C, D)", "rectangle1": "rectangle(E, F, G, H)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EG": "line_segment(E, G)", "line_FH": "line_segment(F, H)"}, "Rels": ["line_extensions_intersect_at(line_AC, line_BD, I)", "line_extensions_intersect_at(line_EG, line_FH, J)", "perpendicular(line_AC, line_BD)", "perpendicular(line_EG, line_FH)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('I'), scene.get_object('B')), 90)"], "possible_solution": {"points": {"A": [5.438452812623582, 1.7831271439997756], "B": [2.45481419206928, -1.5429999278335977], "C": [0.13849303296272453, 1.495449579863477], "D": [2.1671367746874726, 3.756958801496773], "E": [-0.3118045190185168, 0.15789294440305757], "F": [-1.5019805682124159, -1.0488017720572034], "G": [-0.29528600344596095, -2.2389785833639615], "H": [0.8948906949285648, -1.0322835027186106], "I": [2.2835698320389803, 1.6118828143428614], "J": [-0.3035446726252321, -1.0405431333630293]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0077", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is an acute triangle BCD. There is a line segment BC. There is a line segment CD. There is a line segment DB. There is a line segment AD. There is a line segment AC. There is a line segment BD. Line AC is a radius of the circle. Line AD is a radius of the circle. Line AC is perpendicular to line AD. Point D is the midpoint of line BC. Further, the length of line AD is equal to the length of line AC and the angle CAD measures 45 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.acute_triangle(B, C, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_DB = scene.add.line_segment(D, B)\nline_AD = scene.add.line_segment(A, D)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\n\n### relationships\n\nscene.relate.is_radius(line_AC, circle1)\nscene.relate.is_radius(line_AD, circle1)\nscene.relate.perpendicular(line_AC, line_AD)\nscene.relate.is_midpoint(D, line_BC)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_AC.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('C'), scene.get_object('D')), 45)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "acute_triangle(B, C, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_DB": "line_segment(D, B)", "line_AD": "line_segment(A, D)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)"}, "Rels": ["is_radius(line_AC, circle1)", "is_radius(line_AD, circle1)", "perpendicular(line_AC, line_AD)", "is_midpoint(D, line_BC)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_AC').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('C'), scene.get_object('D')), 45)"], "possible_solution": {"points": {"A": [5.761196795637247, 2.7163533985005786], "B": [-9.965574110084967, 9.274868233290327], "C": [6.286443591843297, -4.8866194588597285], "D": [-1.8417762563844466, 2.191108214345047]}, "circles": {"A": 7.621094218840189}}}
{"unique_id": "2obj_4rel_2extra_gen0098", "nl_description": "Diagram description: The diagram contains points A, B, C, D.\nThere is a circle with center A.\nThere is a right triangle BCD.\nThere is a line segment BC.\nThere is a line segment CD.\nThere is a line segment BD.\nThere is a line segment AD.\nThere is a line segment AC.\nPoint B lies on the circle.\nPoint C lies on the circle.\nLine BC is a chord of the circle.\nTriangle BCD is similar to itself.\nFurther, the area of triangle BCD is one-fourth the area of the circle and the angle formed at B by points A, B, and D is 45 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.right_triangle(B, C, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_BD = scene.add.line_segment(B, D)\nline_AD = scene.add.line_segment(A, D)\nline_AC = scene.add.line_segment(A, C)\n\n### relationships\n\nscene.relate.point_lies_on(B, circle1)\nscene.relate.point_lies_on(C, circle1)\nscene.relate.is_chord(line_BC, circle1)\nscene.relate.similar(triangle1, triangle1)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.area, circle1.area / 4)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('D')), 45)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "right_triangle(B, C, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_BD": "line_segment(B, D)", "line_AD": "line_segment(A, D)", "line_AC": "line_segment(A, C)"}, "Rels": ["point_lies_on(B, circle1)", "point_lies_on(C, circle1)", "is_chord(line_BC, circle1)", "similar(triangle1, triangle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('circle1').area / 4)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('D')), 45)"], "possible_solution": {"points": {"A": [0.2554718516997576, -0.8214779268198925], "B": [0.8398740609658806, 1.8873476435452718], "C": [1.6170845455450291, -3.2350381080161665], "D": [3.918962672045521, -2.885778237579587]}, "circles": {"A": 2.771148118145233}}}
{"unique_id": "2obj_4rel_2extra_gen0102", "nl_description": "Diagram description: The diagram contains points A, B, C, O. There is a right isosceles triangle ABC. There is a circle with center O. There is a line segment AB. There is a line segment BC. There is a line segment AC. There is a line segment AO. There is a line segment BO. There is a line segment CO. Line AB intersects the circle at points A and B. Line BC intersects the circle at points B and C. Line AB is congruent to line BC. The circle is the circumcircle of triangle ABC. Further, the length of line AB equals the length of line BC and the length of line AC equals the length of line AB multiplied by the square root of 2.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O = scene.add.points([\"A\", \"B\", \"C\", \"O\"])\n\ntriangleABC = scene.add.right_isosceles_triangle(A, B, C)\ncircleO = scene.add.circle(O)\nlineAB = scene.add.line_segment(A, B)\nlineBC = scene.add.line_segment(B, C)\nlineAC = scene.add.line_segment(A, C)\nlineAO = scene.add.line_segment(A, O)\nlineBO = scene.add.line_segment(B, O)\nlineCO = scene.add.line_segment(C, O)\n\n### relationships\n\nscene.relate.line_intersects_circle_at(lineAB, circleO, A, B)\nscene.relate.line_intersects_circle_at(lineBC, circleO, B, C)\nscene.relate.congruent(lineAB, lineBC)\nscene.relate.is_circumcircle(circleO, triangleABC)\n\n### Extra relationships\n\nscene.constraint.eq(lineAB.length, lineBC.length)\nscene.constraint.eq(lineAC.length, lineAB.length * 2**0.5)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "right_isosceles_triangle(A, B, C)", "circleO": "circle(O)", "lineAB": "line_segment(A, B)", "lineBC": "line_segment(B, C)", "lineAC": "line_segment(A, C)", "lineAO": "line_segment(A, O)", "lineBO": "line_segment(B, O)", "lineCO": "line_segment(C, O)"}, "Rels": ["line_intersects_circle_at(lineAB, circleO, A, B)", "line_intersects_circle_at(lineBC, circleO, B, C)", "congruent(lineAB, lineBC)", "is_circumcircle(circleO, triangleABC)"], "Points": ["A", "B", "C", "O"], "extra_rel": ["scene.constraint.eq(scene.get_object('lineAB').length, scene.get_object('lineBC').length)", "scene.constraint.eq(scene.get_object('lineAC').length, scene.get_object('lineAB').length * 2**0.5)"], "possible_solution": {"points": {"A": [-2.772884587587996, -0.5200432817839472], "B": [-2.276584691800632, -1.723067019443739], "C": [-3.479608420486613, -2.219366908430906], "O": [-3.126246510744098, -1.3697051040835717]}, "circles": {"O": 0.9202118552158426}}}
{"unique_id": "2obj_4rel_2extra_gen0103", "nl_description": "Diagram description: The diagram contains points A, B, C, O, D, E, F. There is a triangle ABC with points A, B, C. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. The circle is the circumcircle of triangle ABC. Point A lies on the circle. Line AD is an altitude of triangle ABC from vertex A. Line BE is an altitude of triangle ABC from vertex B.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"O\", \"D\", \"E\", \"F\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\ncircleO = scene.add.circle(O)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_circumcircle(circleO, triangleABC)\nscene.relate.point_lies_on(A, circleO)\nscene.relate.is_altitude(line_AD, triangleABC, A)\nscene.relate.is_altitude(line_BE, triangleABC, B)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "circleO": "circle(O)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["is_circumcircle(circleO, triangleABC)", "point_lies_on(A, circleO)", "is_altitude(line_AD, triangleABC, A)", "is_altitude(line_BE, triangleABC, B)"], "Points": ["A", "B", "C", "O", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-1.548728346964683, 0.4023096920103074], "B": [-1.0873026584574632, 3.4098728910553318], "C": [0.8448048104304382, 0.19784355789134303], "O": [-0.22904094937192376, 1.739018812117509], "D": [0.11854567493000921, 1.4052121994330973], "E": [-1.3457036006565566, 0.38496619709365376], "F": [-3.3958670659906796, 7.544579308414686]}, "circles": {"O": 1.8783946005177359}}}
{"unique_id": "2obj_4rel_2extra_gen0105", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a minor arc BC with center A. There is a line segment BC. There is a line segment AD. The circle is congruent to itself. Angle BAD is a right angle. Line BC is a chord of the circle. Line AD is a radius of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\nminor_arc1 = scene.add.minor_arc(A, B, C)\nline_BC = scene.add.line_segment(B, C)\nline_AD = scene.add.line_segment(A, D)\n\n### relationships\n\nscene.relate.congruent(circle1, circle1)\nscene.relate.right_angle(B, A, D)\nscene.relate.is_chord(line_BC, circle1)\nscene.relate.is_radius(line_AD, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "minor_arc1": "minor_arc(A, B, C)", "line_BC": "line_segment(B, C)", "line_AD": "line_segment(A, D)"}, "Rels": ["congruent(circle1, circle1)", "right_angle(B, A, D)", "is_chord(line_BC, circle1)", "is_radius(line_AD, circle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": [], "possible_solution": {"points": {"A": [0.07958341994360597, -3.400078940053265], "B": [2.5666820504170254, -0.8687989211609313], "C": [3.43772773726523, -4.54720791211795], "D": [-2.451696594334866, -0.9129803068032248]}, "circles": {"A": 3.5486670920232974}}}
{"unique_id": "2obj_4rel_2extra_gen0111", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a rectangle ABCD. There is a square EFGH. There is a line segment AC. There is a line segment BD. There is a line segment EG. There is a line segment FH. Line AC and line BD intersect at I. Point I lies on line AC. Point I lies on line BD. Line AC is perpendicular to line BD. Further, the area of rectangle ABCD equals the area of square EFGH. Further, angle AIB is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\nsquare1 = scene.add.square(E, F, G, H)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EG = scene.add.line_segment(E, G)\nline_FH = scene.add.line_segment(F, H)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_BD, I)\nscene.relate.point_lies_on(I, line_AC)\nscene.relate.point_lies_on(I, line_BD)\nscene.relate.perpendicular(line_AC, line_BD)\n\n### Extra relationships\n\nscene.constraint.eq(rectangle1.area, square1.area)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('I'), scene.get_object('B')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "square1": "square(E, F, G, H)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EG": "line_segment(E, G)", "line_FH": "line_segment(F, H)"}, "Rels": ["lines_intersect_at(line_AC, line_BD, I)", "point_lies_on(I, line_AC)", "point_lies_on(I, line_BD)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": ["scene.constraint.eq(scene.get_object('rectangle1').area, scene.get_object('square1').area)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('I'), scene.get_object('B')), 90)"], "possible_solution": {"points": {"A": [0.944199648202945, 2.2282673986735437], "B": [-0.6071954427722678, 0.14956820140585797], "C": [-2.685894722681404, 1.7009631746399132], "D": [-1.1344999559928792, 3.7796623472648183], "E": [0.12087398074563988, -2.542915013530791], "F": [-2.463549429344266, -2.7633055998249527], "G": [-2.683939474690478, -0.17888148414723234], "H": [-0.09951647557150467, 0.04150925130709323], "I": [-0.8708475299903147, 1.9646153124867796]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0119", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a square with vertices A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment EA. There is a line segment ED. Line BD is the perpendicular bisector of line AC. The extensions of line AC and line BD intersect at point E. Line EA is a radius of the circle. Line ED is a radius of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nsquare1 = scene.add.square(A, B, C, D)\ncircle1 = scene.add.circle(E)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EA = scene.add.line_segment(E, A)\nline_ED = scene.add.line_segment(E, D)\n\n### relationships\n\nscene.relate.perpendicular_bisector_at(line_AC, line_BD)\nscene.relate.line_extensions_intersect_at(line_AC, line_BD, E)\nscene.relate.is_radius(line_EA, circle1)\nscene.relate.is_radius(line_ED, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"square1": "square(A, B, C, D)", "circle1": "circle(E)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EA": "line_segment(E, A)", "line_ED": "line_segment(E, D)"}, "Rels": ["perpendicular_bisector_at(line_AC, line_BD)", "line_extensions_intersect_at(line_AC, line_BD, E)", "is_radius(line_EA, circle1)", "is_radius(line_ED, circle1)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [0.3257612454035661, 2.601268134733978], "B": [-0.3326283289982287, 1.9193543367156205], "C": [-1.0145421155960677, 2.577743903539535], "D": [-0.3561525539846666, 3.2596576972969435], "E": [-0.3443904399447772, 2.5895059931274242]}, "circles": {"E": 0.670254919735488}}}
{"unique_id": "2obj_4rel_2extra_gen0128", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a square with points A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment AB. There is a line segment CD. Line AC is a diameter of the circle. Line BD is a diameter of the circle. Line AB is parallel to line CD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nsquare1 = scene.add.square(A, B, C, D)\ncircle1 = scene.add.circle(E)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_AB = scene.add.line_segment(A, B)\nline_CD = scene.add.line_segment(C, D)\n\n### relationships\n\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.parallel(line_AB, line_CD)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"square1": "square(A, B, C, D)", "circle1": "circle(E)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_AB": "line_segment(A, B)", "line_CD": "line_segment(C, D)"}, "Rels": ["is_diameter(line_AC, circle1)", "is_diameter(line_BD, circle1)", "parallel(line_AB, line_CD)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [-3.3901028315411503, -1.6135652081703677], "B": [-2.437722748332645, 1.6170796238373362], "C": [0.7929220798286145, 0.6646995504351502], "D": [-0.15945800749085393, -2.5659452941153305], "E": [-1.2985903699961854, -0.4744328383909771]}, "circles": {"E": 2.381605962009867}}}
{"unique_id": "2obj_4rel_2extra_gen0130", "nl_description": "Diagram description: The diagram contains points A, B, C, O. There is a major arc with center A, start point B, and end point C. There is a circle with center O. There is a line segment AB. There is a line segment OC. There is a line segment AC. There is a line segment BC. Line OC is a radius of the circle. Line AB is a chord of the circle. Line AB is perpendicular to line AC. Point C lies on the major arc.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O = scene.add.points([\"A\", \"B\", \"C\", \"O\"])\n\nsemicircle1 = scene.add.major_arc(A, B, C)\ncircle1 = scene.add.circle(O)\nline_AB = scene.add.line_segment(A, B)\nline_OC = scene.add.line_segment(O, C)\nline_AC = scene.add.line_segment(A, C)\nline_BC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.is_radius(line_OC, circle1)\nscene.relate.is_chord(line_AB, circle1)\nscene.relate.perpendicular(line_AB, line_AC)\nscene.relate.point_lies_on(C, semicircle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"semicircle1": "major_arc(A, B, C)", "circle1": "circle(O)", "line_AB": "line_segment(A, B)", "line_OC": "line_segment(O, C)", "line_AC": "line_segment(A, C)", "line_BC": "line_segment(B, C)"}, "Rels": ["is_radius(line_OC, circle1)", "is_chord(line_AB, circle1)", "perpendicular(line_AB, line_AC)", "point_lies_on(C, semicircle1)"], "Points": ["A", "B", "C", "O"], "extra_rel": [], "possible_solution": {"points": {"A": [0.2934028785918443, 0.10643505793481653], "B": [1.7836091612401341, 0.03191564784049895], "C": [0.21888347125827962, -1.3837712230144579], "O": [1.001246308986937, -0.675927802859992]}, "circles": {"O": 1.0550516367568135}}}
{"unique_id": "2obj_4rel_2extra_gen0135", "nl_description": "Diagram description: The diagram contains points A, B, C, O, D, E, F. There is an acute triangle ABC. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. The circle is the circumcircle of triangle ABC. Line AD is an altitude of triangle ABC from vertex A. Line BE is an altitude of triangle ABC from vertex B. Line AD is congruent to line BE. Further, the length of line AD is equal to the length of line BE. The area of triangle ABC is less than or equal to 10.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"O\", \"D\", \"E\", \"F\"])\n\ntriangleABC = scene.add.acute_triangle(A, B, C)\ncircleO = scene.add.circle(O)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_circumcircle(circleO, triangleABC)\nscene.relate.is_altitude(line_AD, triangleABC, A)\nscene.relate.is_altitude(line_BE, triangleABC, B)\nscene.relate.congruent(line_AD, line_BE)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BE.length)\nscene.constraint.leq(triangleABC.area, 10)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "acute_triangle(A, B, C)", "circleO": "circle(O)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["is_circumcircle(circleO, triangleABC)", "is_altitude(line_AD, triangleABC, A)", "is_altitude(line_BE, triangleABC, B)", "congruent(line_AD, line_BE)"], "Points": ["A", "B", "C", "O", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)", "scene.constraint.leq(scene.get_object('triangleABC').area, 10)"], "possible_solution": {"points": {"A": [1.7609701511237845, 1.7433499226271927], "B": [-0.4144797490024337, 0.3614196032344544], "C": [-2.3678520700540644, 5.839718017072741], "O": [-0.7688075684566231, 3.3224802288984443], "D": [-0.6062615451092863, 0.8992769124499517], "E": [1.3556054156725093, 2.1455282542354435], "F": [-10.0, 0.4781947772705064]}, "circles": {"O": 2.9821849989978726}}}
{"unique_id": "2obj_4rel_2extra_gen0152", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, O. There is an obtuse triangle with vertices A, B, C. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is an altitude of triangle ABC from vertex A. Line AD intersects the circle at points A and D. Line BE is an altitude of triangle ABC from vertex B. Line CF is an altitude of triangle ABC from vertex C. Further, the length of line AD is equal to the length of line BE. Further, angle AOD is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, O = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"O\"])\n\ntriangleABC = scene.add.obtuse_triangle(A, B, C)\ncircleO = scene.add.circle(O)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_altitude(line_AD, triangleABC, A)\nscene.relate.line_intersects_circle_at(line_AD, circleO, A, D)\nscene.relate.is_altitude(line_BE, triangleABC, B)\nscene.relate.is_altitude(line_CF, triangleABC, C)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BE.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('O'), scene.get_object('D')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "obtuse_triangle(A, B, C)", "circleO": "circle(O)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["is_altitude(line_AD, triangleABC, A)", "line_intersects_circle_at(line_AD, circleO, A, D)", "is_altitude(line_BE, triangleABC, B)", "is_altitude(line_CF, triangleABC, C)"], "Points": ["A", "B", "C", "D", "E", "F", "O"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('O'), scene.get_object('D')), 90)"], "possible_solution": {"points": {"A": [-3.107949365202667, -0.700973675642732], "B": [1.355841515463132, 4.845788410721938], "C": [2.641092138330121, -0.7580368422675676], "D": [2.3413582112304514, 0.5488369721071444], "E": [1.3003592727901472, -0.7447304934279307], "F": [-0.8760428696581323, 2.072412331772009], "O": [0.24160950885253688, -2.800722029483513]}, "circles": {"O": 3.953288129342314}}}
{"unique_id": "2obj_4rel_2extra_gen0154", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a circle with center A. There is a major arc BC. There is a line segment BD. There is a line segment AC. There is a line segment ED. Line BD is the perpendicular bisector of line AC. Line BD is parallel to line ED. Line BD is a chord of the circle. Point D lies on the circle. Further, the length of line BD is equal to the length of line ED, and angle BAD is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ncircle1 = scene.add.circle(A)\nmajor_arc1 = scene.add.major_arc(A, B, C)\nline_BD = scene.add.line_segment(B, D)\nline_AC = scene.add.line_segment(A, C)\nline_ED = scene.add.line_segment(E, D)\n\n### relationships\n\nscene.relate.perpendicular_bisector_at(line_BD, line_AC)\nscene.relate.parallel(line_BD, line_ED)\nscene.relate.is_chord(line_BD, circle1)\nscene.relate.point_lies_on(D, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(line_BD.length, line_ED.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "major_arc1": "major_arc(A, B, C)", "line_BD": "line_segment(B, D)", "line_AC": "line_segment(A, C)", "line_ED": "line_segment(E, D)"}, "Rels": ["perpendicular_bisector_at(line_BD, line_AC)", "parallel(line_BD, line_ED)", "is_chord(line_BD, circle1)", "point_lies_on(D, circle1)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_BD').length, scene.get_object('line_ED').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 90)"], "possible_solution": {"points": {"A": [1.5929726318789175, -0.6507668513208474], "B": [1.8281155206038202, -0.5724598748896352], "C": [1.7091660732418805, -0.4171613200199233], "D": [1.5172016856795116, -0.42323939130157134], "E": [1.2066169794851676, -0.27309194560224354]}, "circles": {"A": 0.24291763345642767}}}
{"unique_id": "2obj_4rel_2extra_gen0159", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a right triangle with vertices B, C, D. There is a line segment BC. There is a line segment CD. There is a line segment BD. There is a line segment AD. There is a line segment AC. Line BC is perpendicular to line CD. The angle at C formed by points B, C, D is a right angle. Line BD is a chord of the circle. Line AD is a radius of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.right_triangle(B, C, D)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_BD = scene.add.line_segment(B, D)\nline_AD = scene.add.line_segment(A, D)\nline_AC = scene.add.line_segment(A, C)\n\n### relationships\n\nscene.relate.perpendicular(line_BC, line_CD)\nscene.relate.right_angle(B, C, D)\nscene.relate.is_chord(line_BD, circle1)\nscene.relate.is_radius(line_AD, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "right_triangle(B, C, D)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_BD": "line_segment(B, D)", "line_AD": "line_segment(A, D)", "line_AC": "line_segment(A, C)"}, "Rels": ["perpendicular(line_BC, line_CD)", "right_angle(B, C, D)", "is_chord(line_BD, circle1)", "is_radius(line_AD, circle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": [], "possible_solution": {"points": {"A": [0.3757721720859874, 4.39001839930144], "B": [-0.21784684616119926, -0.9756908817477185], "C": [-0.8270063952939416, -1.6787653473497515], "D": [-3.529081481617247, 0.6623733562389547]}, "circles": {"A": 5.398446037889544}}}
{"unique_id": "2obj_4rel_2extra_gen0170", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a major arc with center A and endpoints B and C. There is a quadrilateral with vertices D, E, F, G. There is a line segment DF. There is a line segment EG. There is a line segment DE. There is a line segment FG. Point D lies on the major arc with center A and endpoints B and C. Point F lies on the major arc with center A and endpoints B and C. Points D, F, and G are collinear. Line segment DF is perpendicular to line segment EG.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\nmajor_arc1 = scene.add.major_arc(A, B, C)\nquad1 = scene.add.quadrilateral(D, E, F, G)\nline_DF = scene.add.line_segment(D, F)\nline_EG = scene.add.line_segment(E, G)\nline_DE = scene.add.line_segment(D, E)\nline_FG = scene.add.line_segment(F, G)\n\n### relationships\n\nscene.relate.point_lies_on(D, major_arc1)\nscene.relate.point_lies_on(F, major_arc1)\nscene.relate.collinear(D, F, G)\nscene.relate.perpendicular(line_DF, line_EG)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"major_arc1": "major_arc(A, B, C)", "quad1": "quadrilateral(D, E, F, G)", "line_DF": "line_segment(D, F)", "line_EG": "line_segment(E, G)", "line_DE": "line_segment(D, E)", "line_FG": "line_segment(F, G)"}, "Rels": ["point_lies_on(D, major_arc1)", "point_lies_on(F, major_arc1)", "collinear(D, F, G)", "perpendicular(line_DF, line_EG)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.3755472964981842, 3.904442232860571], "B": [1.0806748986859005, 2.6963020449358557], "C": [0.47882108515559185, 5.592707738701773], "D": [-2.2565930567744976, 4.109021365332825], "E": [2.4085816774383764, 1.6908037479253968], "F": [-1.8251792288436348, 2.688402329576635], "G": [-1.1903306501832955, 0.5978854066389189]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0173", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a trapezoid with vertices A, B, C, D. There is a parallelogram with vertices E, F, G, H. There is a line segment AB. There is a line segment CD. There is a line segment EF. Line AB is parallel to line CD. Line EF is parallel to line CD. Point A lies on line AB. Point B lies on line AB. Point E lies on line EF. Point F lies on line EF. Further, the length of line AB is equal to the length of line CD. Further, the slope of line EF is zero.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntrapezoid1 = scene.add.trapezoid(A, B, C, D)\nparallelogram1 = scene.add.parallelogram(E, F, G, H)\nline_AB = scene.add.line_segment(A, B)\nline_CD = scene.add.line_segment(C, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.parallel(line_AB, line_CD)\nscene.relate.parallel(line_EF, line_CD)\nscene.relate.point_lies_on(A, line_AB)\nscene.relate.point_lies_on(B, line_AB)\nscene.relate.point_lies_on(E, line_EF)\nscene.relate.point_lies_on(F, line_EF)\n\n### Extra relationships\n\nscene.constraint.eq(line_AB.length, line_CD.length)\nscene.constraint.eq(line_EF.slope, 0)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "trapezoid(A, B, C, D)", "parallelogram1": "parallelogram(E, F, G, H)", "line_AB": "line_segment(A, B)", "line_CD": "line_segment(C, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["parallel(line_AB, line_CD)", "parallel(line_EF, line_CD)", "point_lies_on(A, line_AB)", "point_lies_on(B, line_AB)", "point_lies_on(E, line_EF)", "point_lies_on(F, line_EF)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AB').length, scene.get_object('line_CD').length)", "scene.constraint.eq(scene.get_object('line_EF').slope, 0)"], "possible_solution": {"points": {"A": [-1.3409988223784886, 8.550430823986535], "B": [-0.9208258413969304, 8.550430969181336], "C": [2.475447002987507, -5.784644495679235], "D": [2.055274016123179, -5.784644466361385], "E": [-0.7242343508783534, 0.06311303811391718], "F": [5.122849847187396, 0.06311276802900215], "G": [-4.035055786794775, -3.888636669431914], "H": [-9.882139963654113, -3.8886363892949327]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0179", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a minor arc with center A, start point B, and end point C. There is an isosceles trapezoid with vertices D, E, F, G. There is a line segment DF. There is a line segment EG. There is a line segment DE. There is a line segment FG. The extensions of line DF and line EG intersect at point H. Line DE is congruent to line FG. Line DF is perpendicular to line DE. Point C lies on the minor arc.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\narc1 = scene.add.minor_arc(A, B, C)\ntrapezoid1 = scene.add.isosceles_trapezoid(D, E, F, G)\nline_DF = scene.add.line_segment(D, F)\nline_EG = scene.add.line_segment(E, G)\nline_DE = scene.add.line_segment(D, E)\nline_FG = scene.add.line_segment(F, G)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line_DF, line_EG, H)\nscene.relate.congruent(line_DE, line_FG)\nscene.relate.perpendicular(line_DF, line_DE)\nscene.relate.point_lies_on(C, arc1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"arc1": "minor_arc(A, B, C)", "trapezoid1": "isosceles_trapezoid(D, E, F, G)", "line_DF": "line_segment(D, F)", "line_EG": "line_segment(E, G)", "line_DE": "line_segment(D, E)", "line_FG": "line_segment(F, G)"}, "Rels": ["line_extensions_intersect_at(line_DF, line_EG, H)", "congruent(line_DE, line_FG)", "perpendicular(line_DF, line_DE)", "point_lies_on(C, arc1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [0.6520526802332517, 1.534383498647769], "B": [0.8859292525163192, 0.8658308998761488], "C": [-0.03367173254713589, 1.3570619714773098], "D": [0.3219091501020738, 0.4739951004377886], "E": [2.406522499453987, -0.8995539274826939], "F": [0.7001027628331516, 1.0479734891297834], "G": [-1.3845105628674794, 2.421522460125725], "H": [0.5110060485361572, 0.7609842427042692]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0181", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, M, N. There is an equilateral triangle ABC. There is a rhomboid DEFG. There is a line segment AM. There is a line segment BN. There is a line segment CD. There is a line segment EF. Line CD is parallel to line EF. Triangle ABC is similar to triangle ABC. Line AM is an altitude of triangle ABC from vertex A. Line BN is a median of triangle ABC from vertex B. Further, length of line AM is equal to length of line BN and length of line CD is less than or equal to length of line EF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, M, N = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"M\", \"N\"])\n\ntriangle_ABC = scene.add.equilateral_triangle(A, B, C)\nrhomboid_DEFG = scene.add.rhomboid(D, E, F, G)\nline_AM = scene.add.line_segment(A, M)\nline_BN = scene.add.line_segment(B, N)\nline_CD = scene.add.line_segment(C, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.parallel(line_CD, line_EF)\nscene.relate.similar(triangle_ABC, triangle_ABC)\nscene.relate.is_altitude(line_AM, triangle_ABC, A)\nscene.relate.is_median(line_BN, triangle_ABC, B)\n\n### Extra relationships\n\nscene.constraint.eq(line_AM.length, line_BN.length)\nscene.constraint.leq(line_CD.length, line_EF.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle_ABC": "equilateral_triangle(A, B, C)", "rhomboid_DEFG": "rhomboid(D, E, F, G)", "line_AM": "line_segment(A, M)", "line_BN": "line_segment(B, N)", "line_CD": "line_segment(C, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["parallel(line_CD, line_EF)", "similar(triangle_ABC, triangle_ABC)", "is_altitude(line_AM, triangle_ABC, A)", "is_median(line_BN, triangle_ABC, B)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "M", "N"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AM').length, scene.get_object('line_BN').length)", "scene.constraint.leq(scene.get_object('line_CD').length, scene.get_object('line_EF').length)"], "possible_solution": {"points": {"A": [2.4887198177930907, 7.915145611210449], "B": [8.92370591146164, 3.493672657406324], "C": [1.877105194293471, 0.1315482219093413], "D": [0.5348349925207232, -0.20492248650202072], "E": [2.2623824881961174, 0.0688022401416245], "F": [0.0004674779160643403, -0.498198476641309], "G": [-1.7270824352481067, -0.771923750097719], "M": [5.400405254326479, 1.8126101907462575], "N": [2.182912404985614, 4.02334648779818]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0199", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, O. There is an obtuse triangle ABC. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is a diameter of the circle. Point A lies on the circle. Line BE is an altitude of triangle ABC from vertex B. Line CF is an altitude of triangle ABC from vertex C.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, O = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"O\"])\n\ntriangleABC = scene.add.obtuse_triangle(A, B, C)\ncircleO = scene.add.circle(O)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_diameter(line_AD, circleO)\nscene.relate.point_lies_on(A, circleO)\nscene.relate.is_altitude(line_BE, triangleABC, B)\nscene.relate.is_altitude(line_CF, triangleABC, C)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "obtuse_triangle(A, B, C)", "circleO": "circle(O)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["is_diameter(line_AD, circleO)", "point_lies_on(A, circleO)", "is_altitude(line_BE, triangleABC, B)", "is_altitude(line_CF, triangleABC, C)"], "Points": ["A", "B", "C", "D", "E", "F", "O"], "extra_rel": [], "possible_solution": {"points": {"A": [-2.899518459098409, -4.104084857801311], "B": [-4.428013502729438, -5.362186377489895], "C": [0.5707269007751087, 6.031490987351718], "D": [-3.7486590990109283, -1.6779034677480293], "E": [-3.4454520631490575, -5.698598208869561], "F": [4.142440023879793, 1.6921385403837992], "O": [-3.3240887532768872, -2.8909941954055887]}, "circles": {"O": 1.2852427816076253}}}
{"unique_id": "2obj_4rel_2extra_gen0200", "nl_description": "Diagram description: The diagram contains points A, B, C, O, D, E, F, H. There is a scalene triangle ABC. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is an altitude of triangle ABC from vertex A. Line BE is an altitude of triangle ABC from vertex B. Line CF is an altitude of triangle ABC from vertex C. The extensions of line AD and line BE intersect at point H. The circle with center O is the circumcircle of triangle ABC. Further, the inradius of triangle ABC is 1.5. Further, the length of line BE is less than or equal to the length of line CF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O, D, E, F, H = scene.add.points([\"A\", \"B\", \"C\", \"O\", \"D\", \"E\", \"F\", \"H\"])\n\ntriangleABC = scene.add.scalene_triangle(A, B, C)\ncircleO = scene.add.circle(O)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_altitude(line_AD, triangleABC, A)\nscene.relate.is_altitude(line_BE, triangleABC, B)\nscene.relate.line_extensions_intersect_at(line_AD, line_BE, H)\nscene.relate.is_circumcircle(circleO, triangleABC)\n\n### Extra relationships\n\nscene.constraint.eq(triangleABC.inradius, 1.5)\nscene.constraint.leq(line_BE.length, line_CF.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "scalene_triangle(A, B, C)", "circleO": "circle(O)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["is_altitude(line_AD, triangleABC, A)", "is_altitude(line_BE, triangleABC, B)", "line_extensions_intersect_at(line_AD, line_BE, H)", "is_circumcircle(circleO, triangleABC)"], "Points": ["A", "B", "C", "O", "D", "E", "F", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangleABC').inradius, 1.5)", "scene.constraint.leq(scene.get_object('line_BE').length, scene.get_object('line_CF').length)"], "possible_solution": {"points": {"A": [-2.446756806462016, 0.27858177974974474], "B": [1.2197000948539045, -0.26133189345175517], "C": [3.5883759570471208, 9.593217478436959], "O": [0.15200907712605904, 5.207249209945892], "D": [1.1421291997197265, -0.5840556018685096], "E": [-1.6090641283711191, 1.571478800995389], "F": [-8.218784696940386, 4.175019935297569], "H": [2.057301389811364, -0.8040296702137156]}, "circles": {"O": 5.571834960813016}}}
{"unique_id": "2obj_4rel_2extra_gen0204", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a quadrilateral with vertices A, B, C, D. There is a rectangle with vertices E, F, G, H. There is a line segment AC. There is a line segment BD. There is a line segment EG. There is a line segment FH. The extensions of line AC and line BD intersect at point I. The extensions of line EG and line FH intersect at point J. Line AC is perpendicular to line BD. Line EG is perpendicular to line FH. Further, length of line AC is equal to length of line BD and angle A I B is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\"])\n\nquadrilateral1 = scene.add.quadrilateral(A, B, C, D)\nrectangle1 = scene.add.rectangle(E, F, G, H)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EG = scene.add.line_segment(E, G)\nline_FH = scene.add.line_segment(F, H)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line_AC, line_BD, I)\nscene.relate.line_extensions_intersect_at(line_EG, line_FH, J)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.perpendicular(line_EG, line_FH)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('I'), scene.get_object('B')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"quadrilateral1": "quadrilateral(A, B, C, D)", "rectangle1": "rectangle(E, F, G, H)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EG": "line_segment(E, G)", "line_FH": "line_segment(F, H)"}, "Rels": ["line_extensions_intersect_at(line_AC, line_BD, I)", "line_extensions_intersect_at(line_EG, line_FH, J)", "perpendicular(line_AC, line_BD)", "perpendicular(line_EG, line_FH)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('I'), scene.get_object('B')), 90)"], "possible_solution": {"points": {"A": [-3.5652052888632704, -3.960832991452434], "B": [0.7026513938484563, -0.7654137963721285], "C": [-3.4770568691927366, -2.1176153858491884], "D": [2.545869868572683, -0.8535619945883601], "E": [-0.9128348383827299, 0.9091030718783343], "F": [0.3489610950509561, 0.5873152628538186], "G": [0.6707495515521503, 1.8491112835568821], "H": [-0.5910467440573014, 2.170899489729848], "I": [-3.4030012151571745, -0.5690694377254414], "J": [-0.12104302364476216, 1.379106653634376]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0227", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a major arc with center A, start point B, and end point C. There is a minor arc with center D, start point E, and end point F. There is a line segment AB. There is a line segment DF. There is a line segment GH. The line segment GH is the perpendicular bisector of line segment AB. The line segment GH is perpendicular to line segment DF. Point G lies on the major arc with center A, start point B, and end point C. Point H is the midpoint of the minor arc with center D, start point E, and end point F.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\nsemicircle1 = scene.add.major_arc(A, B, C)\nminor_arc1 = scene.add.minor_arc(D, E, F)\nline_AB = scene.add.line_segment(A, B)\nline_DF = scene.add.line_segment(D, F)\nline_perp = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.perpendicular_bisector_at(line_AB, line_perp)\nscene.relate.perpendicular(line_perp, line_DF)\nscene.relate.point_lies_on(G, semicircle1)\nscene.relate.is_midpoint(H, minor_arc1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"semicircle1": "major_arc(A, B, C)", "minor_arc1": "minor_arc(D, E, F)", "line_AB": "line_segment(A, B)", "line_DF": "line_segment(D, F)", "line_perp": "line_segment(G, H)"}, "Rels": ["perpendicular_bisector_at(line_AB, line_perp)", "perpendicular(line_perp, line_DF)", "point_lies_on(G, semicircle1)", "is_midpoint(H, minor_arc1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [1.1479025840931671, 0.3909986087284522], "B": [2.005887965510677, 0.925782599058853], "C": [1.4714135930739625, -0.5668497177875772], "D": [0.8794051572328754, -1.6748705825025951], "E": [-1.4111692535782758, 0.3977584105989275], "F": [3.500953192300944, -0.040854663889977515], "G": [2.0583177983447882, -0.04863425712904446], "H": [1.1541439055786382, 1.4019851791031503]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0244", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, O. There is an isosceles triangle ABC with AB = BC. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD intersects line BE at G. Line BE intersects line CF at H. Line AD is an altitude of triangle ABC from vertex A. Line BE is an altitude of triangle ABC from vertex B. Further, the inradius of triangle ABC is 2. Further, the length of line AD is less than or equal to one-third of the perimeter of triangle ABC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, O = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"O\"])\n\ntriangleABC = scene.add.isosceles_triangle(A, B, C)\ncircleO = scene.add.circle(O)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AD, line_BE, G)\nscene.relate.lines_intersect_at(line_BE, line_CF, H)\nscene.relate.is_altitude(line_AD, triangleABC, A)\nscene.relate.is_altitude(line_BE, triangleABC, B)\n\n### Extra relationships\n\nscene.constraint.eq(triangleABC.inradius, 2.0)\nscene.constraint.leq(line_AD.length, triangleABC.perimeter / 3)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "isosceles_triangle(A, B, C)", "circleO": "circle(O)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["lines_intersect_at(line_AD, line_BE, G)", "lines_intersect_at(line_BE, line_CF, H)", "is_altitude(line_AD, triangleABC, A)", "is_altitude(line_BE, triangleABC, B)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "O"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangleABC').inradius, 2.0)", "scene.constraint.leq(scene.get_object('line_AD').length, scene.get_object('triangleABC').perimeter / 3)"], "possible_solution": {"points": {"A": [1.231170725818509, 0.600717134004501], "B": [-6.403786661702343, 0.06777669381154258], "C": [-0.8032160941613347, -5.148568964522489], "D": [-2.5812495512207385, -3.4925184913337133], "E": [0.21397987306932897, -2.273923033504186], "F": [-2.570987724035803, -0.6612558442295331], "G": [-1.0347170002110961, -1.8320713378526805], "H": [-2.283878398890766, -1.3900549669251148], "O": [0.310590681368373, 3.254296011010867]}, "circles": {"O": 4.244681915571439}}}
{"unique_id": "2obj_4rel_2extra_gen0250", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a right triangle ABC with vertices A, B, C. There is a parallelogram DEFG with vertices D, E, F, G. There is a line segment BD. There is a line segment CF. There is a line segment AC. B lies on line segment BD. F lies on line segment CF. Line segment BD and line segment CF intersect at point C. Line segment BD is perpendicular to line segment CF. Further, length of line AC equals length of line BD. Further, angle BAC is 45 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntriangleABC = scene.add.right_triangle(A, B, C)\nparallelogramDEFG = scene.add.parallelogram(D, E, F, G)\nline_BD = scene.add.line_segment(B, D)\nline_CF = scene.add.line_segment(C, F)\nline_AC = scene.add.line_segment(A, C)\n\n### relationships\n\nscene.relate.point_lies_on(B, line_BD)\nscene.relate.point_lies_on(F, line_CF)\nscene.relate.lines_intersect_at(line_BD, line_CF, C)\nscene.relate.perpendicular(line_BD, line_CF)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 45)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "right_triangle(A, B, C)", "parallelogramDEFG": "parallelogram(D, E, F, G)", "line_BD": "line_segment(B, D)", "line_CF": "line_segment(C, F)", "line_AC": "line_segment(A, C)"}, "Rels": ["point_lies_on(B, line_BD)", "point_lies_on(F, line_CF)", "lines_intersect_at(line_BD, line_CF, C)", "perpendicular(line_BD, line_CF)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 45)"], "possible_solution": {"points": {"A": [1.457085466100029, 3.936714513467677], "B": [6.0022994442899416, 2.847179898662899], "C": [4.912764849747004, -1.6980340628290378], "D": [4.461464901389355, -3.5807233102853298], "E": [4.242169104788123, -0.2094929231954025], "F": [1.1240522072176586, -0.7898406627569822], "G": [1.3433480148012917, -4.161071035890834]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0260", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a circle with center B. There is a line segment CD. There is a line segment EF. There is a line segment GH. circle with center B is a scaled version of the circle with center A with a scale factor of 2. line segment CD is parallel to line segment EF. line segment GH is a diameter of the circle with center A. point C lies on the circle with center A.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ncircle1 = scene.add.circle(A)\ncircle2 = scene.add.circle(B)\nline_CD = scene.add.line_segment(C, D)\nline_EF = scene.add.line_segment(E, F)\nline_GH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.scale(circle1, circle2, 2)\nscene.relate.parallel(line_CD, line_EF)\nscene.relate.is_diameter(line_GH, circle1)\nscene.relate.point_lies_on(C, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "circle2": "circle(B)", "line_CD": "line_segment(C, D)", "line_EF": "line_segment(E, F)", "line_GH": "line_segment(G, H)"}, "Rels": ["scale(circle1, circle2, 2)", "parallel(line_CD, line_EF)", "is_diameter(line_GH, circle1)", "point_lies_on(C, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [-2.2591027529684906, -0.043182203974268314], "B": [-0.39054432615180523, 1.3182193495872432], "C": [-2.002513004180315, -0.03752205591597486], "D": [-1.1401649530383295, -1.1795233634510436], "E": [3.009345191745076, 2.271294242609647], "F": [2.723242140058276, 2.650178430200197], "G": [-2.30735987293384, 0.20889251667249148], "H": [-2.2108460079985317, -0.29525680620897626]}, "circles": {"A": 0.2566521519303229, "B": 0.12832607042049596}}}
{"unique_id": "2obj_4rel_2extra_gen0265", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a major arc with center A and endpoints B and C. There is a semicircle with center D and endpoints E and F. There is a line segment BE. There is a line segment CF. There is a line segment DE. Point B lies on the major arc with center A and endpoints B and C. Point C lies on the major arc with center A and endpoints B and C. Point E lies on the semicircle with center D and endpoints E and F. Point F lies on the semicircle with center D and endpoints E and F. Further, the radius of the major arc is equal to the radius of the semicircle and angle BAC is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\nmajor_arc1 = scene.add.major_arc(A, B, C)\nsemicircle1 = scene.add.semicircle(D, E, F)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_DE = scene.add.line_segment(D, E)\n\n### relationships\n\nscene.relate.point_lies_on(B, major_arc1)\nscene.relate.point_lies_on(C, major_arc1)\nscene.relate.point_lies_on(E, semicircle1)\nscene.relate.point_lies_on(F, semicircle1)\n\n### Extra relationships\n\nscene.constraint.eq(major_arc1.radius, semicircle1.radius)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"major_arc1": "major_arc(A, B, C)", "semicircle1": "semicircle(D, E, F)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_DE": "line_segment(D, E)"}, "Rels": ["point_lies_on(B, major_arc1)", "point_lies_on(C, major_arc1)", "point_lies_on(E, semicircle1)", "point_lies_on(F, semicircle1)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('major_arc1').radius, scene.get_object('semicircle1').radius)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [-0.26667735952801835, 0.9677425670416322], "B": [-0.2116824576235784, -2.8468148917062615], "C": [3.5478801032707032, 1.0227374690538606], "D": [0.19227944526303492, 1.3414559041164678], "E": [3.359130881285068, 3.468642944760916], "F": [-2.9745719891517366, -0.7857311350618391]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0270", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a major arc with center A, start point B, and end point C. There is a trapezoid with vertices D, E, F, G. There is a line segment DF. There is a line segment EG. There is a line segment DE. There is a line segment FG. Angle DFG is a right angle. Line DE is parallel to line FG. Line DF is perpendicular to EG. Point D lies on the major arc with center A, start point B, and end point C.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\nmajor_arc1 = scene.add.major_arc(A, B, C)\ntrapezoid1 = scene.add.trapezoid(D, E, F, G)\nline_DF = scene.add.line_segment(D, F)\nline_EG = scene.add.line_segment(E, G)\nline_DE = scene.add.line_segment(D, E)\nline_FG = scene.add.line_segment(F, G)\n\n### relationships\n\nscene.relate.right_angle(D, F, G)\nscene.relate.parallel(line_DE, line_FG)\nscene.relate.perpendicular(line_DF, line_EG)\nscene.relate.point_lies_on(D, major_arc1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"major_arc1": "major_arc(A, B, C)", "trapezoid1": "trapezoid(D, E, F, G)", "line_DF": "line_segment(D, F)", "line_EG": "line_segment(E, G)", "line_DE": "line_segment(D, E)", "line_FG": "line_segment(F, G)"}, "Rels": ["right_angle(D, F, G)", "parallel(line_DE, line_FG)", "perpendicular(line_DF, line_EG)", "point_lies_on(D, major_arc1)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [2.6719953669256022, 0.0690915423459133], "B": [0.7743425212644642, 2.8879975916711675], "C": [-0.5565470737836649, -0.9910150745823159], "D": [6.0544848172793575, -0.256593444958884], "E": [-2.084735160027953, 2.2858749189086613], "F": [6.1097282233091486, -0.06439481513699898], "G": [6.308129575822479, -0.12636923339416756]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0274", "nl_description": "Diagram description: The diagram contains points A, B, C, D. There is a circle with center A. There is a right isosceles triangle BCD. There is a line segment AC. There is a line segment BC. There is a line segment CD. Line AC and line BC intersect at point C. Angle ACD is acute. Line BC is a chord of the circle. Line AC is a radius of the circle. Further, the area of the circle equals the perimeter of the triangle and angle ACD is 45 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D = scene.add.points([\"A\", \"B\", \"C\", \"D\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.right_isosceles_triangle(B, C, D)\nline_AC = scene.add.line_segment(A, C)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_BC, C)\nscene.relate.acute_angle(A, C, D)\nscene.relate.is_chord(line_BC, circle1)\nscene.relate.is_radius(line_AC, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(circle1.area, triangle1.perimeter)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('C'), scene.get_object('D')), 45)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "right_isosceles_triangle(B, C, D)", "line_AC": "line_segment(A, C)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)"}, "Rels": ["lines_intersect_at(line_AC, line_BC, C)", "acute_angle(A, C, D)", "is_chord(line_BC, circle1)", "is_radius(line_AC, circle1)"], "Points": ["A", "B", "C", "D"], "extra_rel": ["scene.constraint.eq(scene.get_object('circle1').area, scene.get_object('triangle1').perimeter)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('C'), scene.get_object('D')), 45)"], "possible_solution": {"points": {"A": [1.0376982346881694, 1.05080406089767], "B": [0.896628558776721, 2.5812525347341295], "C": [2.5681465437751303, 1.1918737337553347], "D": [1.178767919870178, -0.4796442276596979]}, "circles": {"A": 1.5369361304577203}}}
{"unique_id": "2obj_4rel_2extra_gen0279", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a triangle with vertices A, B, C. There is an acute triangle with vertices D, E, F. There is a line segment AG. There is a line segment BH. There is a line segment IJ. Line AG is an altitude of triangle ABC from vertex A. Line BH is a median of triangle ABC from vertex B. Line AG intersects line BH at G. Line IJ is the perpendicular bisector of line BH.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\nacute_triangleDEF = scene.add.acute_triangle(D, E, F)\nline_altitude = scene.add.line_segment(A, G)\nline_median = scene.add.line_segment(B, H)\nline_perp_bisector = scene.add.line_segment(I, J)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude, triangleABC, A)\nscene.relate.is_median(line_median, triangleABC, B)\nscene.relate.lines_intersect_at(line_altitude, line_median, G)\nscene.relate.perpendicular_bisector_at(line_median, line_perp_bisector)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "Triangle(A, B, C)", "acute_triangleDEF": "AcuteTriangle(D, E, F)", "line_altitude": "line_segment(A, G)", "line_median": "line_segment(B, H)", "line_perp_bisector": "line_segment(I, J)"}, "Rels": ["is_altitude(line_altitude, triangleABC, A)", "is_median(line_median, triangleABC, B)", "lines_intersect_at(line_altitude, line_median, G)", "perpendicular_bisector_at(line_median, line_perp_bisector)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J"], "extra_rel": [], "possible_solution": {"points": {"A": [3.328745638407081, -4.90180302082613], "B": [3.3154353473587768, -5.187770795708777], "C": [-9.815539618039304, 8.873368848966958], "D": [9.68999951800373, -2.7556225636238554], "E": [-4.684299542360186, -2.15660080550782], "F": [-10.0, 6.02483240233652], "G": [3.1805131468539627, -5.040236697627702], "H": [-3.2434318755426443, 1.9857360069244678], "I": [1.6116297933200878, 2.361981238995131], "J": [-4.051913585056608, -2.816300328601285]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0287", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There is a major arc BC. There are line segments BD and CE. The extensions of line BD and line CE intersect at point F. Line BD is parallel to line CE. Point B lies on the circle. Point C lies on the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\nmajor_arc1 = scene.add.major_arc(A, B, C)\nline1 = scene.add.line_segment(B, D)\nline2 = scene.add.line_segment(C, E)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line1, line2, F)\nscene.relate.parallel(line1, line2)\nscene.relate.point_lies_on(B, circle1)\nscene.relate.point_lies_on(C, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "major_arc1": "major_arc(A, B, C)", "line1": "line_segment(B, D)", "line2": "line_segment(C, E)"}, "Rels": ["line_extensions_intersect_at(line1, line2, F)", "parallel(line1, line2)", "point_lies_on(B, circle1)", "point_lies_on(C, circle1)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.9553726197083777, 0.9495920691192553], "B": [-3.30177177720661, -1.0758429798313938], "C": [1.289879319703374, 3.0866039735844604], "D": [-0.6489934668982502, 1.328967142677067], "E": [-3.809514719792646, -1.5361247207509534], "F": [-1.3131861050624596, 0.7268598333333183]}, "circles": {"A": 3.0996735490961047}}}
{"unique_id": "2obj_4rel_2extra_gen0291", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a circle with center A. There is a circle with center B. There is a line segment CD. There is a line segment AB. There is a line segment EF. Point C lies on the circle with center A. Point D lies on the circle with center A. Line CD is a chord of the circle with center A. Line AB is perpendicular to line CD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\ncircle1 = scene.add.circle(A)\ncircle2 = scene.add.circle(B)\nline_CD = scene.add.line_segment(C, D)\nline_AB = scene.add.line_segment(A, B)\nline EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.point_lies_on(C, circle1)\nscene.relate.point_lies_on(D, circle1)\nscene.relate.is_chord(line_CD, circle1)\nscene.relate.perpendicular(line_AB, line_CD)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "circle2": "circle(B)", "line_CD": "line_segment(C, D)", "line_AB": "line_segment(A, B)", "line EF": "line_segment(E, F)"}, "Rels": ["point_lies_on(C, circle1)", "point_lies_on(D, circle1)", "is_chord(line_CD, circle1)", "perpendicular(line_AB, line_CD)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [2.599499881167229, -2.762022121411526], "B": [2.2722343280320048, -2.499726769194888], "C": [2.1347619639567172, 0.3825362834673445], "D": [-0.5707984270494609, -2.9931877299052463], "E": [6.51196327110449, 3.4572983405870663], "F": [-7.882413282137635, 3.390526532619916]}, "circles": {"A": 3.1787149758219417, "B": 7.399636745595005}}}
{"unique_id": "2obj_4rel_2extra_gen0298", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a minor arc with center A from B to C. There is a rhombus with vertices D, E, F, G. There is a line segment DF. There is a line segment GE. There is a line segment AC. Line DF and line GE intersect at H. H is the midpoint of line AC. Line DF is perpendicular to line GE. Point B lies on the minor arc with center A from B to C. Further, the perimeter of the rhombus is equal to four times the length of line DF and the inscribed angle of the minor arc is 45 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\narc1 = scene.add.minor_arc(A, B, C)\nrhombus1 = scene.add.rhombus(D, E, F, G)\nline_DF = scene.add.line_segment(D, F)\nline_GE = scene.add.line_segment(G, E)\nline_AC = scene.add.line_segment(A, C)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_DF, line_GE, H)\nscene.relate.is_midpoint(H, line_AC)\nscene.relate.perpendicular(line_DF, line_GE)\nscene.relate.point_lies_on(B, arc1)\n\n### Extra relationships\n\nscene.constraint.eq(rhombus1.perimeter, 4 * line_DF.length)\nscene.constraint.eq(arc1.inscribed_angle, 45)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"arc1": "minor_arc(A, B, C)", "rhombus1": "rhombus(D, E, F, G)", "line_DF": "line_segment(D, F)", "line_GE": "line_segment(G, E)", "line_AC": "line_segment(A, C)"}, "Rels": ["lines_intersect_at(line_DF, line_GE, H)", "is_midpoint(H, line_AC)", "perpendicular(line_DF, line_GE)", "point_lies_on(B, arc1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('rhombus1').perimeter, 4 * scene.get_object('line_DF').length)", "scene.constraint.eq(scene.get_object('arc1').inscribed_angle, 45)"], "possible_solution": {"points": {"A": [3.055697138383929, -4.397332812435128], "B": [-1.6658795835848776, -4.986412063497957], "C": [2.4666181285329882, 0.32424366095885887], "D": [2.7219248243000336, -1.7564363114289416], "E": [3.246329356652168, -1.9685873172093695], "F": [2.800400282919208, -2.316655715932538], "G": [2.27599707594219, -2.104506874777397], "H": [2.761156760641656, -2.036542535482256]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0317", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a circle with center B. There is a line segment CD. There is a line segment AB. There is a line segment EF. The extensions of line segment CD and line segment AB intersect at point G. Line segment AB is the perpendicular bisector of line segment CD. Line segment CD is a chord of the circle with center A. Line segment EF is tangent to the circle with center B at point H.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ncircle1 = scene.add.circle(A)\ncircle2 = scene.add.circle(B)\nline_CD = scene.add.line_segment(C, D)\nline_AB = scene.add.line_segment(A, B)\nline EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line_CD, line_AB, G)\nscene.relate.perpendicular_bisector_at(line_CD, line_AB)\nscene.relate.is_chord(line_CD, circle1)\nscene.relate.tangent_to_circle(line EF, circle2, H)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "circle2": "circle(B)", "line_CD": "line_segment(C, D)", "line_AB": "line_segment(A, B)", "line EF": "line_segment(E, F)"}, "Rels": ["line_extensions_intersect_at(line_CD, line_AB, G)", "perpendicular_bisector_at(line_CD, line_AB)", "is_chord(line_CD, circle1)", "tangent_to_circle(line EF, circle2, H)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [1.5191431343344282, 1.6168863503100481], "B": [1.0661564269842119, 1.365992564355153], "C": [2.155938362145385, -0.06722089740586437], "D": [0.4293611922544106, 3.0500998576465985], "E": [-2.717805590899545, 0.27775352315356705], "F": [-0.2763586288968755, -5.090966577320849], "G": [1.2926484590440996, 1.4914415489643997], "H": [-2.479450761595618, -0.2463865471739513]}, "circles": {"A": 1.80047929040238, "B": 3.8950091879007736}}}
{"unique_id": "2obj_4rel_2extra_gen0322", "nl_description": "Diagram description: The diagram contains points A, B, C, O. There is a right triangle with vertices A, B, C. There is a circle with center O. There is a line segment AB. There is a line segment BC. There is a line segment AC. There is a line segment OA. There is a line segment OC. Line AC is a diameter of the circle. The extension of line AB intersects the circle at points A and B. Line OA is a radius of the circle. Line OC is a radius of the circle. Further, length of line AB is equal to length of line BC. Further, the angle ABC is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O = scene.add.points([\"A\", \"B\", \"C\", \"O\"])\n\nright_triangle_ABC = scene.add.right_triangle(A, B, C)\ncircle_O = scene.add.circle(O)\nline_AB = scene.add.line_segment(A, B)\nline_BC = scene.add.line_segment(B, C)\nline_AC = scene.add.line_segment(A, C)\nline_OA = scene.add.line_segment(O, A)\nline_OC = scene.add.line_segment(O, C)\n\n### relationships\n\nscene.relate.is_diameter(line_AC, circle_O)\nscene.relate.line_extension_intersects_circle_at(line_AB, circle_O, A, B)\nscene.relate.is_radius(line_OA, circle_O)\nscene.relate.is_radius(line_OC, circle_O)\n\n### Extra relationships\n\nscene.constraint.eq(line_AB.length, line_BC.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"right_triangle_ABC": "right_triangle(A, B, C)", "circle_O": "circle(O)", "line_AB": "line_segment(A, B)", "line_BC": "line_segment(B, C)", "line_AC": "line_segment(A, C)", "line_OA": "line_segment(O, A)", "line_OC": "line_segment(O, C)"}, "Rels": ["is_diameter(line_AC, circle_O)", "line_extension_intersects_circle_at(line_AB, circle_O, A, B)", "is_radius(line_OA, circle_O)", "is_radius(line_OC, circle_O)"], "Points": ["A", "B", "C", "O"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AB').length, scene.get_object('line_BC').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [0.10938142377247594, -2.779435000670724], "B": [-2.048476989762858, 0.7295956219991963], "C": [1.460553639193907, 2.8874540375852105], "O": [0.7849675328524129, 0.05400951817900403]}, "circles": {"O": 2.9128721927370687}}}
{"unique_id": "2obj_4rel_2extra_gen0329", "nl_description": "Diagram description: The diagram contains points A, B, C, O. There is a right triangle ABC with vertices A, B, C. There is a circle with center O. There is a line segment AC. There is a line segment BC. There is a line segment AB. There is a line segment OA. There is a line segment OC. Line AC is a diameter of the circle. Point A lies on the circle. Point C lies on the circle. Line OA is a radius of the circle. Further, the area of triangle ABC is equal to 6 and the inradius of triangle ABC is equal to 1.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O = scene.add.points([\"A\", \"B\", \"C\", \"O\"])\n\ntriangleABC = scene.add.right_triangle(A, B, C)\ncircleO = scene.add.circle(O)\nline_AC = scene.add.line_segment(A, C)\nline_BC = scene.add.line_segment(B, C)\nline_AB = scene.add.line_segment(A, B)\nline_OA = scene.add.line_segment(O, A)\nline_OC = scene.add.line_segment(O, C)\n\n### relationships\n\nscene.relate.is_diameter(line_AC, circleO)\nscene.relate.point_lies_on(A, circleO)\nscene.relate.point_lies_on(C, circleO)\nscene.relate.is_radius(line_OA, circleO)\n\n### Extra relationships\n\nscene.constraint.eq(triangleABC.area, 6)\nscene.constraint.eq(triangleABC.inradius, 1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "right_triangle(A, B, C)", "circleO": "circle(O)", "line_AC": "line_segment(A, C)", "line_BC": "line_segment(B, C)", "line_AB": "line_segment(A, B)", "line_OA": "line_segment(O, A)", "line_OC": "line_segment(O, C)"}, "Rels": ["is_diameter(line_AC, circleO)", "point_lies_on(A, circleO)", "point_lies_on(C, circleO)", "is_radius(line_OA, circleO)"], "Points": ["A", "B", "C", "O"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangleABC').area, 6)", "scene.constraint.eq(scene.get_object('triangleABC').inradius, 1)"], "possible_solution": {"points": {"A": [-4.391930401029768, -2.806614377665557], "B": [-0.5535495610526375, -1.6810520014936547], "C": [-1.3977183124805073, 1.197723213385558], "O": [-2.894824398812311, -0.8044455630909982]}, "circles": {"O": 2.500001282653487}}}
{"unique_id": "2obj_4rel_2extra_gen0330", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a kite ABCD. There is a circle with center E. There are line segments AC, BD, AB, CD. Line AB is tangent to the circle at point A. Line AC and line BD intersect at point E. Line AC is a diameter of the circle. Line AC is perpendicular to line BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nkite1 = scene.add.kite(A, B, C, D)\ncircle1 = scene.add.circle(E)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_AB = scene.add.line_segment(A, B)\nline_CD = scene.add.line_segment(C, D)\n\n### relationships\n\nscene.relate.tangent_to_circle(line_AB, circle1, A)\nscene.relate.lines_intersect_at(line_AC, line_BD, E)\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.perpendicular(line_AC, line_BD)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"kite1": "kite(A, B, C, D)", "circle1": "circle(E)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_AB": "line_segment(A, B)", "line_CD": "line_segment(C, D)"}, "Rels": ["tangent_to_circle(line_AB, circle1, A)", "lines_intersect_at(line_AC, line_BD, E)", "is_diameter(line_AC, circle1)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [1.4514294488497712, -4.414802037962624], "B": [-4.647928732395239, 8.320439640567784], "C": [1.0883836609164854, -4.582403121647567], "D": [2.1838906056034832, -6.47835253550875], "E": [1.271121830362348, -4.501152723752806]}, "circles": {"E": 0.19994074160853786}}}
{"unique_id": "2obj_4rel_2extra_gen0338", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a rectangle with A, B, C, D. There is a circle with center E. There is a line segment AC. There is a line segment BD. There is a line segment AB. There is a line segment BC. Line AC intersects the circle at points A and C. Line BD extends to intersect the circle at points B and D. Line AC is a diameter of the circle. Line AB is perpendicular to line BC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\ncircle1 = scene.add.circle(E)\nline_AC = scene.add.line_segment(A, C)\nline BD = scene.add.line_segment(B, D)\nline_AB = scene.add.line_segment(A, B)\nline_BC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.line_intersects_circle_at(line_AC, circle1, A, C)\nscene.relate.line_extension_intersects_circle_at(line BD, circle1, B, D)\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.perpendicular(line_AB, line_BC)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "circle1": "circle(E)", "line_AC": "line_segment(A, C)", "line BD": "line_segment(B, D)", "line_AB": "line_segment(A, B)", "line_BC": "line_segment(B, C)"}, "Rels": ["line_intersects_circle_at(line_AC, circle1, A, C)", "line_extension_intersects_circle_at(line BD, circle1, B, D)", "is_diameter(line_AC, circle1)", "perpendicular(line_AB, line_BC)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [-1.762493323192021, 1.4196274319909954], "B": [-1.0806107435229215, -0.7557666470702645], "C": [-2.5237094082644087, -1.208109431484454], "D": [-3.2055919699387805, 0.9672846509484813], "E": [-2.1431013486969595, 0.10575900377596929]}, "circles": {"E": 1.3678862357930242}}}
{"unique_id": "2obj_4rel_2extra_gen0339", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a major arc with center A, start point B, end point C. There is an isosceles triangle with vertices D, E, F. There is a line segment DE. There is a line segment DF. There is a line segment EF. There is a line segment AD. Point D lies on the major arc. Line segment DE and line segment AD intersect at point D. Line segment DF is an altitude of the isosceles triangle DEF originating from vertex D. Line segment DE is perpendicular to line segment DF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\nmajor_arc1 = scene.add.major_arc(A, B, C)\nisosceles_triangle1 = scene.add.isosceles_triangle(D, E, F)\nline_DE = scene.add.line_segment(D, E)\nline_DF = scene.add.line_segment(D, F)\nline EF = scene.add.line_segment(E, F)\nline_AD = scene.add.line_segment(A, D)\n\n### relationships\n\nscene.relate.point_lies_on(D, major_arc1)\nscene.relate.lines_intersect_at(line_DE, line_AD, D)\nscene.relate.is_altitude(line_DF, isosceles_triangle1, D)\nscene.relate.perpendicular(line_DE, line_DF)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"major_arc1": "major_arc(A, B, C)", "isosceles_triangle1": "isosceles_triangle(D, E, F)", "line_DE": "line_segment(D, E)", "line_DF": "line_segment(D, F)", "line EF": "line_segment(E, F)", "line_AD": "line_segment(A, D)"}, "Rels": ["point_lies_on(D, major_arc1)", "lines_intersect_at(line_DE, line_AD, D)", "is_altitude(line_DF, isosceles_triangle1, D)", "perpendicular(line_DE, line_DF)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [-4.210598797405376, -0.7134239374801193], "B": [-7.802354343915406, -9.93258995601578], "C": [5.490478869647776, -2.658375374648615], "D": [-6.903820375540258, 8.807094611308738], "E": [5.61592160698248, -6.186253763142405], "F": [-6.74979658456716, 8.935668157612156]}, "circles": {}}}
{"unique_id": "2obj_4rel_2extra_gen0344", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a circle with center B. There is a line segment CD. There is a line segment EF. There is a line segment AH. The extensions of line CD and line EF intersect at point G. Line AH is a radius of the circle with center A. Line CD is perpendicular to line EF. Point H lies on the circle with center A. Further, the diameter of the circle with center A is 6 units and the length of line CD is less than or equal to the diameter of the circle with center A.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ncircle1 = scene.add.circle(A)\ncircle2 = scene.add.circle(B)\nline_CD = scene.add.line_segment(C, D)\nline_EF = scene.add.line_segment(E, F)\nline_AH = scene.add.line_segment(A, H)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line_CD, line_EF, G)\nscene.relate.is_radius(line_AH, circle1)\nscene.relate.perpendicular(line_CD, line_EF)\nscene.relate.point_lies_on(H, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(circle1.diameter, 6)\nscene.constraint.leq(line_CD.length, circle1.diameter)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "circle2": "circle(B)", "line_CD": "line_segment(C, D)", "line_EF": "line_segment(E, F)", "line_AH": "line_segment(A, H)"}, "Rels": ["line_extensions_intersect_at(line_CD, line_EF, G)", "is_radius(line_AH, circle1)", "perpendicular(line_CD, line_EF)", "point_lies_on(H, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('circle1').diameter, 6)", "scene.constraint.leq(scene.get_object('line_CD').length, scene.get_object('circle1').diameter)"], "possible_solution": {"points": {"A": [0.3733957257316957, 0.9454679822761622], "B": [-2.443095575193106, -8.601546501256928], "C": [2.3658653505368417, -2.180257610310739], "D": [0.3263969189009244, 2.1579725964915384], "E": [-6.635611886567996, 0.36793782636453487], "F": [-1.0825701716642615, 2.978507739244487], "G": [-0.24455714344508864, 3.3724704954668607], "H": [1.4618326225185658, -1.8501186608812785]}, "circles": {"A": 2.999999922912509, "B": 10.0}}}
{"unique_id": "3obj_4rel_1extra_gen0001", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M, N, O. There is a scalene triangle with vertices A, B, C. There is a rectangle with vertices D, E, F, G. There is a square with vertices H, I, J, K. There is a line segment AL. There is a line segment CM. There is a line segment BN. There is a line segment HO. Line AL is an altitude of triangle ABC from vertex A. Line CM is an altitude of triangle ABC from vertex C. Line BN is perpendicular to line HO. Triangle ABC is similar to itself.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K, L, M, N, O = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"L\", \"M\", \"N\", \"O\"])\n\ntriangleABC = scene.add.scalene_triangle(A, B, C)\nrectangleDEFG = scene.add.rectangle(D, E, F, G)\nsquareHIJK = scene.add.square(H, I, J, K)\nline_AL = scene.add.line_segment(A, L)\nline_CM = scene.add.line_segment(C, M)\nline_BN = scene.add.line_segment(B, N)\nline_HO = scene.add.line_segment(H, O)\n\n### relationships\n\nscene.relate.is_altitude(line_AL, triangleABC, A)\nscene.relate.is_altitude(line_CM, triangleABC, C)\nscene.relate.similar(triangleABC, triangleABC)\nscene.relate.perpendicular(line_BN, line_HO)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "scalene_triangle(A, B, C)", "rectangleDEFG": "rectangle(D, E, F, G)", "squareHIJK": "square(H, I, J, K)", "line_AL": "line_segment(A, L)", "line_CM": "line_segment(C, M)", "line_BN": "line_segment(B, N)", "line_HO": "line_segment(H, O)"}, "Rels": ["is_altitude(line_AL, triangleABC, A)", "is_altitude(line_CM, triangleABC, C)", "similar(triangleABC, triangleABC)", "perpendicular(line_BN, line_HO)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O"], "extra_rel": [], "possible_solution": {"points": {"A": [0.24827555619008157, -0.031222467757802977], "B": [-5.219753270939753, 1.851488679708736], "C": [8.98627819767034, -0.9468629934763869], "D": [0.1613916359571769, 1.3677905586854304], "E": [-0.5327630951312108, 1.3957064953893616], "F": [-0.5245066917684026, 1.6010192318122975], "G": [0.1696482539574127, 1.5731039077844011], "H": [1.899550979207579, -0.5948765732818759], "I": [1.574923978915804, -0.1797993117434206], "J": [1.1598474566340495, -0.5044262674366596], "K": [1.4844745829406298, -0.9195024684726625], "L": [0.4010376613121733, 0.7442864124405197], "M": [8.342021373611304, -2.818001209503993], "N": [-4.799734784419052, 2.755006187703244], "O": [3.579627951440748, -1.37589515516645]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0009", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I.\nThere is a circle with center A.\nThere is a regular pentagon with vertices E, F, G, H, I.\nThere is a triangle with vertices B, C, D.\nPoint B lies on the circle.\nPoint C lies on the circle.\nThere is an acute angle at D with arms DB and DC.\nThe circle is the circumcircle of triangle BCD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.triangle(B, C, D)\npentagon1 = scene.add.regular_pentagon(E, F, G, H, I)\n\n### relationships\n\nscene.relate.point_lies_on(B, circle1)\nscene.relate.point_lies_on(C, circle1)\nscene.relate.acute_angle(D, B, C)\nscene.relate.is_circumcircle(circle1, triangle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "triangle(B, C, D)", "pentagon1": "regular_pentagon(E, F, G, H, I)"}, "Rels": ["point_lies_on(B, circle1)", "point_lies_on(C, circle1)", "acute_angle(D, B, C)", "is_circumcircle(circle1, triangle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.3807603409251231, -1.4319277527373944], "B": [-0.8118454101035084, -1.0550407986667274], "C": [-0.118687357243523, -1.9410405726251534], "D": [0.17249413485806295, -1.5795339870040475], "E": [-10.220790958945516, 1.77175443849442], "F": [-15.605532790672783, -5.656670060656859], "G": [-10.204658001273804, -13.07337327995713], "H": [-1.4819919807155386, -10.228723454804182], "I": [-1.49196269689572, -1.053929957467945]}, "circles": {"A": 0.5726064165780875}}}
{"unique_id": "3obj_4rel_1extra_gen0017", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M, N. There is a quadrilateral with vertices A, B, C, D. There is a rectangle with vertices E, F, G, H. There is a right trapezoid with vertices I, J, K, L. There is a line segment AC. There is a line segment BD. There is a line segment EG. There is a line segment FH. M is the midpoint of line AC. N is the midpoint of line BD. The angle ABC is a right angle. Line AC is perpendicular to line BD. Further, the length of line BD is equal to the length of line EG.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K, L, M, N = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"L\", \"M\", \"N\"])\n\nquadrilateral1 = scene.add.quadrilateral(A, B, C, D)\nrectangle1 = scene.add.rectangle(E, F, G, H)\nright_trapezoid1 = scene.add.right_trapezoid(I, J, K, L)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EG = scene.add.line_segment(E, G)\nline_FH = scene.add.line_segment(F, H)\n\n### relationships\n\nscene.relate.is_midpoint(M, line_AC)\nscene.relate.is_midpoint(N, line_BD)\nscene.relate.right_angle(A, B, C)\nscene.relate.perpendicular(line_AC, line_BD)\n\n### Extra relationships\n\nscene.constraint.eq(line_BD.length, line_EG.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"quadrilateral1": "quadrilateral(A, B, C, D)", "rectangle1": "rectangle(E, F, G, H)", "right_trapezoid1": "right_trapezoid(I, J, K, L)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EG": "line_segment(E, G)", "line_FH": "line_segment(F, H)"}, "Rels": ["is_midpoint(M, line_AC)", "is_midpoint(N, line_BD)", "right_angle(A, B, C)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_BD').length, scene.get_object('line_EG').length)"], "possible_solution": {"points": {"A": [-1.899193017012983, -2.388447672808922], "B": [-1.7083120788837287, -2.240935893168942], "C": [-2.1163885788367733, -1.7128826440552736], "D": [-0.8998714141038706, -1.9810201325570642], "E": [0.8986293500381354, 1.1099586521729747], "F": [0.6906269372582674, 1.4085542392272712], "G": [0.061048632032438106, 0.9699888317440217], "H": [0.26905114358910737, 0.671393163245091], "I": [3.656638799678926, 0.5649035005571164], "J": [3.307999013943686, 1.2861628682613881], "K": [1.8441666831224082, 0.6480073061353305], "L": [2.2200095801813244, -0.1295292482094575], "M": [-2.0077907504731276, -2.0506649524503984], "N": [-1.3040918215804054, -2.1109782688169005]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0019", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, M, N. There is a quadrilateral ABCD. There is an equilateral triangle EFG. There is a quadrilateral HIJK. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment FG. There is a line segment GH. Line AC intersects line BD at point M. Quadrilateral HIJK is the mirror image of quadrilateral ABCD across line EF. Line AC is perpendicular to line BD. Line GH intersects line EF at point N. Further, the area of quadrilateral ABCD equals the area of equilateral triangle EFG. Further, the length of line AC is less than or equal to the length of line BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K, M, N = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"M\", \"N\"])\n\nquad1 = scene.add.quadrilateral(A, B, C, D)\ntri1 = scene.add.equilateral_triangle(E, F, G)\nquad2 = scene.add.quadrilateral(H, I, J, K)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\nline_FG = scene.add.line_segment(F, G)\nline_GH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_BD, M)\nscene.relate.mirror_across_line(quad1, quad2, line_EF)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.lines_intersect_at(line_EF, line_GH, N)\n\n### Extra relationships\n\nscene.constraint.eq(quad1.area, tri1.area)\nscene.constraint.leq(line_AC.length, line_BD.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"quad1": "quadrilateral(A, B, C, D)", "tri1": "equilateral_triangle(E, F, G)", "quad2": "quadrilateral(H, I, J, K)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)", "line_FG": "line_segment(F, G)", "line_GH": "line_segment(G, H)"}, "Rels": ["lines_intersect_at(line_AC, line_BD, M)", "mirror_across_line(quad1, quad2, line_EF)", "perpendicular(line_AC, line_BD)", "lines_intersect_at(line_EF, line_GH, N)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "M", "N"], "extra_rel": ["scene.constraint.eq(scene.get_object('quad1').area, scene.get_object('tri1').area)", "scene.constraint.leq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)"], "possible_solution": {"points": {"A": [0.579858725656235, -1.4139427747270013], "B": [0.9015966786368514, -0.7120535520803722], "C": [-0.1320963575932993, -0.8221290517750931], "D": [-0.10334891940494689, -1.9210066500009586], "E": [-0.4095806961428422, -1.875700833193077], "F": [0.8431824248021679, -1.5422314295137125], "G": [-0.07198982493343438, -0.6240391642553456], "H": [0.6784865549921696, -1.7844544797337698], "I": [1.3065888683086462, -2.233506347765706], "J": [0.3549635889008703, -2.6518968614903535], "K": [-0.1664000443926406, -1.6841489677762616], "M": [0.42509119848639965, -1.285290810118197], "N": [0.5690290271876112, -1.6152071385191167]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0021", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a major arc ABC with center A. There is a right trapezoid DEFG. There is a circle with center H. There is a line segment DE. There is a line segment EF. There is a line segment HB. Line DE is perpendicular to line EF. Point I is the midpoint of line DE. Line HB is a radius of the circle. Point B lies on the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\nmajor_arc1 = scene.add.major_arc(A, B, C)\nright_trap1 = scene.add.right_trapezoid(D, E, F, G)\ncircle1 = scene.add.circle(H)\nline_DE = scene.add.line_segment(D, E)\nline_EF = scene.add.line_segment(E, F)\nline_HB = scene.add.line_segment(H, B)\n\n### relationships\n\nscene.relate.perpendicular(line_DE, line_EF)\nscene.relate.is_midpoint(I, line_DE)\nscene.relate.is_radius(line_HB, circle1)\nscene.relate.point_lies_on(B, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"major_arc1": "major_arc(A, B, C)", "right_trap1": "right_trapezoid(D, E, F, G)", "circle1": "circle(H)", "line_DE": "line_segment(D, E)", "line_EF": "line_segment(E, F)", "line_HB": "line_segment(H, B)"}, "Rels": ["perpendicular(line_DE, line_EF)", "is_midpoint(I, line_DE)", "is_radius(line_HB, circle1)", "point_lies_on(B, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": [], "possible_solution": {"points": {"A": [3.665824681397427, 0.19972015787984487], "B": [-0.3771958124456399, -1.5868134358753019], "C": [0.13450280789721566, 2.8581939357922477], "D": [-0.05734243383218603, 2.3766990159345953], "E": [-0.8207035467042448, 3.1974857312874625], "F": [-1.0856416576407224, 2.9510838398109613], "G": [-0.3222804566910255, 2.130297041916683], "H": [1.8142334575672645, -0.018047449483824314], "I": [-0.439022992486869, 2.787092402027008]}, "circles": {"H": 2.695067520407981}}}
{"unique_id": "3obj_4rel_1extra_gen0037", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L. There is a square with vertices A, B, C, D. There is a rectangle with vertices E, F, G, H. There is a trapezoid with vertices I, J, K, L. There is a line segment AC. There is a line segment EG. There is a line segment IK. There is a line segment JL. There is a right angle at A between AB and AD. Points A, C, and E are collinear. Line AC is parallel to line EG. Line IK is perpendicular to line JL. Further, the length of line AC is equal to the length of line EG and the area of trapezoid IJKL is less than or equal to 12 square units.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K, L = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"L\"])\n\nsquare1 = scene.add.square(A, B, C, D)\nrectangle1 = scene.add.rectangle(E, F, G, H)\ntrapezoid1 = scene.add.trapezoid(I, J, K, L)\nline_AC = scene.add.line_segment(A, C)\nline_EG = scene.add.line_segment(E, G)\nline_IK = scene.add.line_segment(I, K)\nline_JL = scene.add.line_segment(J, L)\n\n### relationships\n\nscene.relate.right_angle(B, A, D)\nscene.relate.collinear(A, C, E)\nscene.relate.parallel(line_AC, line_EG)\nscene.relate.perpendicular(line_IK, line_JL)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_EG.length)\nscene.constraint.leq(trapezoid1.area, 12.0)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"square1": "square(A, B, C, D)", "rectangle1": "rectangle(E, F, G, H)", "trapezoid1": "trapezoid(I, J, K, L)", "line_AC": "line_segment(A, C)", "line_EG": "line_segment(E, G)", "line_IK": "line_segment(I, K)", "line_JL": "line_segment(J, L)"}, "Rels": ["right_angle(B, A, D)", "collinear(A, C, E)", "parallel(line_AC, line_EG)", "perpendicular(line_IK, line_JL)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_EG').length)", "scene.constraint.leq(scene.get_object('trapezoid1').area, 12.0)"], "possible_solution": {"points": {"A": [-0.7982523543995123, -0.31600279683619975], "B": [0.14770650814011232, -0.18374890351643094], "C": [0.27996027518368305, -1.1297076896563851], "D": [-0.6659986065135555, -1.2619614497667715], "E": [0.4454648605390933, -1.2546106020919328], "F": [-0.7527325327921229, -0.9952826471673623], "G": [-0.6327477829580864, -0.4409055584604724], "H": [0.5654493470283377, -0.7002332372775717], "I": [-2.706194046155376, 0.6621369069826477], "J": [-2.503899205460112, 0.5009008664834189], "K": [-3.6401342759733004, 0.40247523508765415], "L": [-2.1452757340640107, -0.7889800850684361]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0041", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a circle with center A. There is a kite with vertices B, C, D, E. There is a minor arc with center A, start point F, and end point G. There is a line segment BE. There is a line segment CD. There is a line segment AF. There is a line segment AG. Line BE is a chord of the circle. Line BE is congruent to line CD. Further, the length of line BE is equal to the length of line CD. Further, the central angle of the minor arc FG is 90 degrees. Further, the length of line AF is less than or equal to the diameter of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ncircle1 = scene.add.circle(A)\nkite1 = scene.add.kite(B, C, D, E)\nminor_arc1 = scene.add.minor_arc(A, F, G)\nline_BE = scene.add.line_segment(B, E)\nline_CD = scene.add.line_segment(C, D)\nline_AF = scene.add.line_segment(A, F)\nline_AG = scene.add.line_segment(A, G)\n\n### relationships\n\nscene.relate.is_chord(line_BE, circle1)\nscene.relate.congruent(line_BE, line_CD)\nscene.relate.point_lies_on(F, circle1)\nscene.relate.point_lies_on(G, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(line_BE.length, line_CD.length)\nscene.constraint.eq(minor_arc1.central_angle, 90)\nscene.constraint.leq(line_AF.length, circle1.diameter)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "kite1": "kite(B, C, D, E)", "minor_arc1": "minor_arc(A, F, G)", "line_BE": "line_segment(B, E)", "line_CD": "line_segment(C, D)", "line_AF": "line_segment(A, F)", "line_AG": "line_segment(A, G)"}, "Rels": ["is_chord(line_BE, circle1)", "congruent(line_BE, line_CD)", "point_lies_on(F, circle1)", "point_lies_on(G, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_BE').length, scene.get_object('line_CD').length)", "scene.constraint.eq(scene.get_object('minor_arc1').central_angle, 90)", "scene.constraint.leq(scene.get_object('line_AF').length, scene.get_object('circle1').diameter)"], "possible_solution": {"points": {"A": [3.009179312953721, -0.621300101929193], "B": [1.2495894466413777, -3.193440851339712], "C": [2.9955953626686367, -8.315329830004329], "D": [3.4319589350250834, -2.921641046565721], "E": [1.6859513150010332, 2.2002477659024535], "F": [0.20205178350145397, 0.732251013735285], "G": [1.655628257489572, -3.4284275054738473]}, "circles": {"A": 3.116418605036179}}}
{"unique_id": "3obj_4rel_1extra_gen0042", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a major arc with center A, from B to C. There is a parallelogram with vertices D, E, F, G. There is a circle with center H. There is a line segment AD. There is a line segment HF. There is a line segment AC. Line HF is a radius of the circle. Line AD is tangent to the circle at point A. Line AC is a chord of the circle. Line AD is perpendicular to line AC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\nsemicircle1 = scene.add.major_arc(A, B, C)\nparallelogram1 = scene.add.parallelogram(D, E, F, G)\ncircle1 = scene.add.circle(H)\nline_AD = scene.add.line_segment(A, D)\nline_HF = scene.add.line_segment(H, F)\nline_AC = scene.add.line_segment(A, C)\n\n### relationships\n\nscene.relate.is_radius(line_HF, circle1)\nscene.relate.tangent_to_circle(line_AD, circle1, A)\nscene.relate.is_chord(line_AC, circle1)\nscene.relate.perpendicular(line_AD, line_AC)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"semicircle1": "major_arc(A, B, C)", "parallelogram1": "parallelogram(D, E, F, G)", "circle1": "circle(H)", "line_AD": "line_segment(A, D)", "line_HF": "line_segment(H, F)", "line_AC": "line_segment(A, C)"}, "Rels": ["is_radius(line_HF, circle1)", "tangent_to_circle(line_AD, circle1, A)", "is_chord(line_AC, circle1)", "perpendicular(line_AD, line_AC)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [1.3439685015036786, 0.30162287432784524], "B": [5.487111116635106, -0.5456278508696637], "C": [-2.665498892521131, -1.0428605265659736], "D": [1.6424417350934615, -0.5884728120136025], "E": [2.0017303708674907, 0.8453773325680326], "F": [-0.8224756923597858, -2.4788679059844165], "G": [-1.1817643377959046, -3.9127181072684354], "H": [-0.6607652777713829, -0.3706184369056609]}, "circles": {"H": 2.11444218597893}}}
{"unique_id": "3obj_4rel_1extra_gen0063", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, O. There is a right triangle ABC. There is a rhombus ABDE. There is a circle with center O. There are line segments AC, BE, and OA. Line OA is a radius of the circle. Point O is the midpoint of line AC. Line AC is perpendicular to line BE. The circle is the circumcircle of right triangle ABC. Further, length of line BE equals half the length of line AC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, O = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"O\"])\n\ntriangleABC = scene.add.right_triangle(A, B, C)\nrhombusABDE = scene.add.rhombus(A, B, D, E)\ncircleO = scene.add.circle(O)\nline_AC = scene.add.line_segment(A, C)\nline_BE = scene.add.line_segment(B, E)\nline_OA = scene.add.line_segment(O, A)\n\n### relationships\n\nscene.relate.is_radius(line_OA, circleO)\nscene.relate.is_midpoint(O, line_AC)\nscene.relate.perpendicular(line_AC, line_BE)\nscene.relate.is_circumcircle(circleO, triangleABC)\n\n### Extra relationships\n\nscene.constraint.eq(line_BE.length, line_AC.length / 2)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "right_triangle(A, B, C)", "rhombusABDE": "rhombus(A, B, D, E)", "circleO": "circle(O)", "line_AC": "line_segment(A, C)", "line_BE": "line_segment(B, E)", "line_OA": "line_segment(O, A)"}, "Rels": ["is_radius(line_OA, circleO)", "is_midpoint(O, line_AC)", "perpendicular(line_AC, line_BE)", "is_circumcircle(circleO, triangleABC)"], "Points": ["A", "B", "C", "D", "E", "O"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_BE').length, scene.get_object('line_AC').length / 2)"], "possible_solution": {"points": {"A": [1.7236821908133753, 0.9792032348001543], "B": [1.4383403859438426, 1.3681281263551082], "C": [-0.013146922872123408, 0.30321795928393647], "D": [1.4909911692250652, 0.8886385090872573], "E": [1.7763329212231143, 0.4997134359093311], "O": [0.855267841493489, 0.6412108272128181]}, "circles": {"O": 0.9318703611305434}}}
{"unique_id": "3obj_4rel_1extra_gen0064", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a triangle ABC. There is a triangle DEF. There is a major arc with center G, start point H, and end point I. There is a line segment AC. There is a line segment DF. Point A lies on the major arc GHI. Point C lies on the major arc GHI. Triangle ABC is similar to triangle DEF. Line AC is perpendicular to line DF. Further, area of triangle ABC is equal to area of triangle DEF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\ntriangle_ABC = scene.add.triangle(A, B, C)\ntriangle_DEF = scene.add.triangle(D, E, F)\nmajor_arc_GHI = scene.add.major_arc(G, H, I)\nline_AC = scene.add.line_segment(A, C)\nline_DF = scene.add.line_segment(D, F)\n\n### relationships\n\nscene.relate.point_lies_on(A, major_arc_GHI)\nscene.relate.point_lies_on(C, major_arc_GHI)\nscene.relate.similar(triangle_ABC, triangle_DEF)\nscene.relate.perpendicular(line_AC, line_DF)\n\n### Extra relationships\n\nscene.constraint.eq(triangle_ABC.area, triangle_DEF.area)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle_ABC": "triangle(A, B, C)", "triangle_DEF": "triangle(D, E, F)", "major_arc_GHI": "major_arc(G, H, I)", "line_AC": "line_segment(A, C)", "line_DF": "line_segment(D, F)"}, "Rels": ["point_lies_on(A, major_arc_GHI)", "point_lies_on(C, major_arc_GHI)", "similar(triangle_ABC, triangle_DEF)", "perpendicular(line_AC, line_DF)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle_ABC').area, scene.get_object('triangle_DEF').area)"], "possible_solution": {"points": {"A": [0.9319756113574666, 1.7703916188649422], "B": [3.27969480907394, 3.6182688458495265], "C": [1.1843260545020535, 1.1476028932110078], "D": [1.3446575319534808, -1.966787527577502], "E": [1.0371225706749747, 1.0050525278557676], "F": [0.7218655519025206, -2.21912914223193], "G": [1.4523834021140345, 1.6187568271433062], "H": [1.3850894474913162, 1.0808698704182833], "I": [1.4292750892420156, 2.160347338967654]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0066", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M, N, O. There is a major arc with center A and endpoints B and C. There is a regular octagon with vertices D, E, F, G, H, I, J, K. There is a triangle with vertices L, M, N. There is a line segment OM. There is a line segment LN. There is a line segment MN. Angle LMN is obtuse. Point O is the midpoint of line LN. The major arc is symmetric across line OM. Line MN is an altitude of triangle LMN from vertex M. Further, the area of triangle LMN equals the inradius of the regular octagon.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K, L, M, N, O = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"L\", \"M\", \"N\", \"O\"])\n\nmajor_arc1 = scene.add.major_arc(A, B, C)\nregular_octagon1 = scene.add.regular_octagon(D, E, F, G, H, I, J, K)\ntriangle1 = scene.add.triangle(L, M, N)\nline_OM = scene.add.line_segment(O, M)\nline_LN = scene.add.line_segment(L, N)\nline_MN = scene.add.line_segment(M, N)\n\n### relationships\n\nscene.relate.obtuse_angle(L, M, N)\nscene.relate.is_midpoint(O, line_LN)\nscene.relate.mirror_across_line(major_arc1, major_arc1, line_OM)\nscene.relate.is_altitude(line_MN, triangle1, M)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.area, regular_octagon1.inradius)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"major_arc1": "major_arc(A, B, C)", "regular_octagon1": "regular_octagon(D, E, F, G, H, I, J, K)", "triangle1": "triangle(L, M, N)", "line_OM": "line_segment(O, M)", "line_LN": "line_segment(L, N)", "line_MN": "line_segment(M, N)"}, "Rels": ["obtuse_angle(L, M, N)", "is_midpoint(O, line_LN)", "mirror_across_line(major_arc1, major_arc1, line_OM)", "is_altitude(line_MN, triangle1, M)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('regular_octagon1').inradius)"], "possible_solution": {"points": {"A": [-3.4826452020085235, -4.177380330796903], "B": [-4.383350268055579, -5.326948730162612], "C": [-2.5819751281880556, -3.027784690779275], "D": [-9.29012994434174, -0.5550326724013037], "E": [-9.812015518917153, -2.06451950473983], "F": [-9.113675972444492, -3.500916708783916], "G": [-7.604189140105966, -4.022802283359329], "H": [-6.16779193606188, -3.324462736886669], "I": [-5.645906361486467, -1.8149759045481426], "J": [-6.344245907959127, -0.37857870050405684], "K": [-7.853732740297653, 0.1433068740713568], "L": [-6.925354643606997, -8.245742238800872], "M": [5.066021403800161, 6.733794347261027], "N": [5.222911666267387, 6.608226884287963], "O": [-0.851232622802161, -0.8187350628349468]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0067", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, M. There is a rhombus with vertices A, B, C, D. There is a quadrilateral with vertices E, F, G, H. There are line segments AC, BD, EF, and GH. The rhombus is similar to the quadrilateral. Line AC intersects line BD at point M. Line AC is perpendicular to line BD. Line EF is parallel to line GH. Further, the slope of line AC is equal to the slope of line EF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, M = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"M\"])\n\nrhombus1 = scene.add.rhombus(A, B, C, D)\nquad1 = scene.add.quadrilateral(E, F, G, H)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\nline_GH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.similar(rhombus1, quad1)\nscene.relate.lines_intersect_at(line_AC, line_BD, M)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.parallel(line_EF, line_GH)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.slope, line_EF.slope)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rhombus1": "rhombus(A, B, C, D)", "quad1": "quadrilateral(E, F, G, H)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)", "line_GH": "line_segment(G, H)"}, "Rels": ["similar(rhombus1, quad1)", "lines_intersect_at(line_AC, line_BD, M)", "perpendicular(line_AC, line_BD)", "parallel(line_EF, line_GH)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "M"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').slope, scene.get_object('line_EF').slope)"], "possible_solution": {"points": {"A": [2.438540418919796, -1.6153620641091386], "B": [2.2887838723063965, -0.8789237942368879], "C": [2.98947105526781, -1.1505857314082566], "D": [3.1392424545758226, -1.8870493772337456], "E": [-0.6296226370998291, -0.5381907317261908], "F": [0.9604747141997749, 0.8032917991242211], "G": [1.2308076084579893, -1.2594468488241322], "H": [-0.35933176314011167, -2.6009985332917145], "M": [2.7140403146174763, -1.3829469027087793]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0073", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a right triangle BCD. There is a quadrilateral EFGH. There is a line segment BC. There is a line segment CD. There is a line segment AG. There is a line segment EH. Line AG is a radius of the circle. Points A, G, and H are collinear. Line BC is a chord of the circle. Line BC is perpendicular to line CD. Further, the perimeter of right triangle BCD is equal to 12 units and the length of line BC is less than or equal to 5 units.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ncircle1 = scene.add.circle(A)\nright_triangle1 = scene.add.right_triangle(B, C, D)\nquadrilateral1 = scene.add.quadrilateral(E, F, G, H)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_AG = scene.add.line_segment(A, G)\nline_EH = scene.add.line_segment(E, H)\n\n### relationships\n\nscene.relate.is_radius(line_AG, circle1)\nscene.relate.collinear(A, G, H)\nscene.relate.is_chord(line_BC, circle1)\nscene.relate.perpendicular(line_BC, line_CD)\n\n### Extra relationships\n\nscene.constraint.eq(right_triangle1.perimeter, 12.0)\nscene.constraint.leq(line_BC.length, 5.0)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "right_triangle1": "right_triangle(B, C, D)", "quadrilateral1": "quadrilateral(E, F, G, H)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_AG": "line_segment(A, G)", "line_EH": "line_segment(E, H)"}, "Rels": ["is_radius(line_AG, circle1)", "collinear(A, G, H)", "is_chord(line_BC, circle1)", "perpendicular(line_BC, line_CD)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('right_triangle1').perimeter, 12.0)", "scene.constraint.leq(scene.get_object('line_BC').length, 5.0)"], "possible_solution": {"points": {"A": [2.546932239689959, -1.7931464199104707], "B": [2.9251920965111764, -4.275256146559001], "C": [4.213839567120232, 0.08445023306262382], "D": [1.9692998083030782, 0.7478941050986279], "E": [7.523662984221925, -5.973682542466387], "F": [-2.361110872518508, 7.195948946191219], "G": [1.1962483722967514, 0.3233606734715298], "H": [-1.6200441787684334, 4.7364608131859]}, "circles": {"A": 2.5107666509091384}}}
{"unique_id": "3obj_4rel_1extra_gen0090", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a parallelogram with vertices A, B, C, D. There is a right triangle with vertices E, F, G. There is a circle with center H. There is a line segment AC. There is a line segment BD. There is a line segment HF. There is a line segment FG. There is a line segment EG. Line segment AC and line segment BD intersect at point I. Line segment HF and line segment FG intersect at point F. Line segment AC is a diameter of the circle. Line segment HF is a radius of the circle. Further, the length of line segment HF is equal to the length of line segment FG.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\nparallelogram1 = scene.add.parallelogram(A, B, C, D)\nright_triangle1 = scene.add.right_triangle(E, F, G)\ncircle1 = scene.add.circle(H)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_HF = scene.add.line_segment(H, F)\nline_FG = scene.add.line_segment(F, G)\nline_EG = scene.add.line_segment(E, G)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line_AC, line_BD, I)\nscene.relate.line_extensions_intersect_at(line_HF, line_FG, F)\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.is_radius(line_HF, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(line_HF.length, line_FG.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"parallelogram1": "parallelogram(A, B, C, D)", "right_triangle1": "right_triangle(E, F, G)", "circle1": "circle(H)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_HF": "line_segment(H, F)", "line_FG": "line_segment(F, G)", "line_EG": "line_segment(E, G)"}, "Rels": ["line_extensions_intersect_at(line_AC, line_BD, I)", "line_extensions_intersect_at(line_HF, line_FG, F)", "is_diameter(line_AC, circle1)", "is_radius(line_HF, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_HF').length, scene.get_object('line_FG').length)"], "possible_solution": {"points": {"A": [2.2123721353575783, 0.9877490924429966], "B": [-1.2929086215726837, 7.751546036128598], "C": [2.719931897967402, -0.0031110065325974795], "D": [6.275309018598712, -6.863648527960163], "E": [-3.1695520451991124, -2.2602238922358184], "F": [2.874596797765818, 0.8705095274946714], "G": [3.130667446840436, 0.3761414053383171], "H": [2.4660879836802874, 0.4923203402201083], "I": [2.357833334721473, 0.7015083970019258]}, "circles": {"H": 0.556688467225041}}}
{"unique_id": "3obj_4rel_1extra_gen0095", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M, N, O. There is a regular heptagon with vertices A, B, C, D, E, F, G. There is a rhomboid with vertices H, I, J, K. There is a rhomboid with vertices L, M, N, O. There is a line segment AC. There is a line segment HI. There is a line segment HK. There is a line segment MN. The rhomboid with vertices H, I, J, K is a mirror image of the rhomboid with vertices L, M, N, O across line AC. The extensions of line segment HI and line segment MN intersect at point B. Line segment HI is perpendicular to line segment HK. Angle H I K is acute. Further, the area of the rhomboid with vertices H, I, J, K is equal to one third of the area of the regular heptagon with vertices A, B, C, D, E, F, G.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K, L, M, N, O = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"L\", \"M\", \"N\", \"O\"])\n\nheptagon1 = scene.add.regular_heptagon(A, B, C, D, E, F, G)\nrhomboid1 = scene.add.rhomboid(H, I, J, K)\nrhomboid2 = scene.add.rhomboid(L, M, N, O)\nline_AC = scene.add.line_segment(A, C)\nline_HI = scene.add.line_segment(H, I)\nline_HK = scene.add.line_segment(H, K)\nline_MN = scene.add.line_segment(M, N)\n\n### relationships\n\nscene.relate.mirror_across_line(rhomboid1, rhomboid2, line_AC)\nscene.relate.line_extensions_intersect_at(line_HI, line_MN, B)\nscene.relate.perpendicular(line_HI, line_HK)\nscene.relate.acute_angle(H, I, K)\n\n### Extra relationships\n\nscene.constraint.eq(rhomboid1.area, heptagon1.area / 3)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"heptagon1": "regular_heptagon(A, B, C, D, E, F, G)", "rhomboid1": "rhomboid(H, I, J, K)", "rhomboid2": "rhomboid(L, M, N, O)", "line_AC": "line_segment(A, C)", "line_HI": "line_segment(H, I)", "line_HK": "line_segment(H, K)", "line_MN": "line_segment(M, N)"}, "Rels": ["mirror_across_line(rhomboid1, rhomboid2, line_AC)", "line_extensions_intersect_at(line_HI, line_MN, B)", "perpendicular(line_HI, line_HK)", "acute_angle(H, I, K)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O"], "extra_rel": ["scene.constraint.eq(scene.get_object('rhomboid1').area, scene.get_object('heptagon1').area / 3)"], "possible_solution": {"points": {"A": [-1.879764565925493, -1.5316038436576895], "B": [-2.663806346301744, -1.9439787985306034], "C": [-2.830240678296524, -2.8140789249042584], "D": [-2.253739115276106, -3.4867010808112826], "E": [-1.368419092683624, -3.4553470638621575], "F": [-0.8409446447685299, -2.743627088324962], "G": [-1.0685147893287585, -1.8874808122209101], "H": [-2.542376481695984, -1.6307605638388396], "I": [-2.737357331975162, -2.133749043271876], "J": [-4.3803401027127125, -1.4968325089485939], "K": [-4.1853734444977935, -0.9938436029815003], "L": [-1.7818682363098552, -2.1944108607054877], "M": [-2.2063691344543472, -2.5272815228158008], "N": [-1.1189980225748024, -3.9138849650985614], "O": [-0.6944843106060764, -3.5810340961852054]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0104", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a circle with center A. There is a rhombus with vertices B, C, D, E. There is a parallelogram with vertices F, G, H, I. There are line segments BC, CD, FG, GH. Line BC is parallel to line FG. Line CD is perpendicular to line BC. Line CD is a chord of the circle. Line FG is a diameter of the circle. Further, the area of the rhombus equals the area of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\ncircle1 = scene.add.circle(A)\nrhombus1 = scene.add.rhombus(B, C, D, E)\nparallelogram1 = scene.add.parallelogram(F, G, H, I)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_FG = scene.add.line_segment(F, G)\nline_GH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.parallel(line_BC, line_FG)\nscene.relate.perpendicular(line_CD, line_BC)\nscene.relate.is_chord(line_CD, circle1)\nscene.relate.is_diameter(line_FG, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(rhombus1.area, circle1.area)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "rhombus1": "rhombus(B, C, D, E)", "parallelogram1": "parallelogram(F, G, H, I)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_FG": "line_segment(F, G)", "line_GH": "line_segment(G, H)"}, "Rels": ["parallel(line_BC, line_FG)", "perpendicular(line_CD, line_BC)", "is_chord(line_CD, circle1)", "is_diameter(line_FG, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": ["scene.constraint.eq(scene.get_object('rhombus1').area, scene.get_object('circle1').area)"], "possible_solution": {"points": {"A": [-0.5860458344685183, 0.5254952499063693], "B": [-3.579347591288124, 1.0514198930431977], "C": [-1.3856905843772496, 1.5040291478182504], "D": [-0.933081027426837, -0.6896264873702855], "E": [-3.1267377148000146, -1.142235117633902], "F": [0.6515921157093069, 0.7808522369291324], "G": [-1.8236840152171776, 0.27013835016906707], "H": [-2.5989785228278373, 0.9816556747145486], "I": [-0.1237034016016609, 1.4923694806281105]}, "circles": {"A": 1.2637071999496163}}}
{"unique_id": "3obj_4rel_1extra_gen0107", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a circle with center A. There is a circle with center B. There is an obtuse triangle with vertices A, B, C. There are line segments AD, BE, and CF. Line AD is a radius of the circle with center A. Points A, D, and G are collinear. Line BE is an altitude of the obtuse triangle ABC from vertex B. Line CF is a median of the obtuse triangle ABC from vertex C. Further, length of line BE is equal to length of line AD, and angle ABC is 120 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ncircle1 = scene.add.circle(A)\ncircle2 = scene.add.circle(B)\ntriangleABC = scene.add.obtuse_triangle(A, B, C)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_radius(line_AD, circle1)\nscene.relate.collinear(A, D, G)\nscene.relate.is_altitude(line_BE, triangleABC, B)\nscene.relate.is_median(line_CF, triangleABC, C)\n\n### Extra relationships\n\nscene.constraint.eq(line_BE.length, line_AD.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 120)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "circle2": "circle(B)", "triangleABC": "obtuse_triangle(A, B, C)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["is_radius(line_AD, circle1)", "collinear(A, D, G)", "is_altitude(line_BE, triangleABC, B)", "is_median(line_CF, triangleABC, C)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_BE').length, scene.get_object('line_AD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 120)"], "possible_solution": {"points": {"A": [4.116748935265861, -5.738943297711831], "B": [-1.5283086907690977, 0.830757139422696], "C": [0.20311975147698563, 5.766939061244875], "D": [2.8288713998096466, -2.7781531571108085], "E": [1.5284637929369425, 1.8704923885508018], "F": [1.29421983727457, -2.4540931420906227], "G": [1.1833783010083374, 1.0047844064848073]}, "circles": {"A": 3.2287624575250238, "B": 6.8728983904683085}}}
{"unique_id": "3obj_4rel_1extra_gen0111", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F. There is a parallelogram with vertices A, B, C, D. There is a circle with center E. There is a circle with center F. There are line segments AC, BD, and EF. The angle BAD is acute. The extension of line AC intersects the circle with center E at points A and C. Line AC is a diameter of the circle with center E. Line AC is perpendicular to line BD. Further, the area of the circle with center E is equal to the area of the circle with center F and the perimeter of the parallelogram with vertices A, B, C, D is less than or equal to 20.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\"])\n\nparallelogram1 = scene.add.parallelogram(A, B, C, D)\ncircle1 = scene.add.circle(E)\ncircle2 = scene.add.circle(F)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.acute_angle(B, A, D)\nscene.relate.line_extension_intersects_circle_at(line_AC, circle1, A, C)\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.perpendicular(line_AC, line_BD)\n\n### Extra relationships\n\nscene.constraint.eq(circle1.area, circle2.area)\nscene.constraint.leq(parallelogram1.perimeter, 20)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"parallelogram1": "parallelogram(A, B, C, D)", "circle1": "circle(E)", "circle2": "circle(F)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line EF": "line_segment(E, F)"}, "Rels": ["acute_angle(B, A, D)", "line_extension_intersects_circle_at(line_AC, circle1, A, C)", "is_diameter(line_AC, circle1)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F"], "extra_rel": ["scene.constraint.eq(scene.get_object('circle1').area, scene.get_object('circle2').area)", "scene.constraint.leq(scene.get_object('parallelogram1').perimeter, 20)"], "possible_solution": {"points": {"A": [-1.561809311893335, -0.5631094291768933], "B": [-1.4463361074644119, -1.6902780541808227], "C": [-0.33143677336095156, -1.8923754115751843], "D": [-0.4469095386986485, -0.7652060749941829], "E": [-0.9466230663796906, -1.2277423437169324], "F": [-10.0, 7.243812280235875]}, "circles": {"E": 0.9056439918612879, "F": 0.9056440034092125}}}
{"unique_id": "3obj_4rel_1extra_gen0112", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a triangle with vertices A, B, C. There is a triangle with vertices D, E, F. There is a minor arc with center G, start point H, and end point I. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment GH. There is a line segment HI. Triangle ABC is a scaled version of triangle DEF with a scaling factor of 2. Points A, D, and G are collinear. Line AD is perpendicular to line BE. Line CF is an altitude of triangle ABC originating from vertex C. Further, the area of the minor arc is equal to the area of triangle ABC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\ntriangle1 = scene.add.triangle(A, B, C)\ntriangle2 = scene.add.triangle(D, E, F)\narc1 = scene.add.minor_arc(G, H, I)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_GH = scene.add.line_segment(G, H)\nline_HI = scene.add.line_segment(H, I)\n\n### relationships\n\nscene.relate.scale(triangle1, triangle2, 2)\nscene.relate.collinear(A, D, G)\nscene.relate.perpendicular(line_AD, line_BE)\nscene.relate.is_altitude(line_CF, triangle1, C)\n\n### Extra relationships\n\nscene.constraint.eq(arc1.area, triangle1.area)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "triangle(A, B, C)", "triangle2": "triangle(D, E, F)", "arc1": "minor_arc(G, H, I)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_GH": "line_segment(G, H)", "line_HI": "line_segment(H, I)"}, "Rels": ["scale(triangle1, triangle2, 2)", "collinear(A, D, G)", "perpendicular(line_AD, line_BE)", "is_altitude(line_CF, triangle1, C)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": ["scene.constraint.eq(scene.get_object('arc1').area, scene.get_object('triangle1').area)"], "possible_solution": {"points": {"A": [-1.9053421332904252, -1.0846289347047469], "B": [-1.4009116087869684, -0.5401842495774059], "C": [-0.072407494668497, -1.0899243641549863], "D": [-1.5932234438640116, -0.9200112712601831], "E": [-1.2250253230656856, -0.8736684243361031], "F": [-1.0613387195815411, -0.1736747821199961], "G": [3.9391660969426225, 1.9978813689512755], "H": [2.9392354602328297, 2.6259700603948977], "I": [3.598860027025991, 3.1286106385117507]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0113", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is an equilateral triangle with vertices A, B, C. There is a circle with center D. There is a circle with center E. There are line segments AD, BE, AC, and BC. Line AD is a radius of the circle with center D. Line BE is a radius of the circle with center E. Line AC is tangent to the circle with center D at point A. Line BC intersects the circle with center E at points B and C. Further, the inradius of the equilateral triangle equals the radius of the circle with center D.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ntriangle1 = scene.add.equilateral_triangle(A, B, C)\ncircle1 = scene.add.circle(D)\ncircle2 = scene.add.circle(E)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_AC = scene.add.line_segment(A, C)\nline_BC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.is_radius(line_AD, circle1)\nscene.relate.is_radius(line_BE, circle2)\nscene.relate.tangent_to_circle(line_AC, circle1, A)\nscene.relate.line_intersects_circle_at(line_BC, circle2, B, C)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.inradius, circle1.radius)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "equilateral_triangle(A, B, C)", "circle1": "circle(D)", "circle2": "circle(E)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_AC": "line_segment(A, C)", "line_BC": "line_segment(B, C)"}, "Rels": ["is_radius(line_AD, circle1)", "is_radius(line_BE, circle2)", "tangent_to_circle(line_AC, circle1, A)", "line_intersects_circle_at(line_BC, circle2, B, C)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').inradius, scene.get_object('circle1').radius)"], "possible_solution": {"points": {"A": [1.860684099858289, 1.2549176110455524], "B": [-0.490844726404068, 2.7617512574517096], "C": [-0.6200366204557047, -0.028149305726966094], "D": [2.2310735677657534, 0.5387953160453266], "E": [0.22796900592289115, 1.3305236516810413]}, "circles": {"D": 0.8062378679768015, "E": 1.6015947375359585}}}
{"unique_id": "3obj_4rel_1extra_gen0120", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, O, P, Q, R, S, T, U. There is a triangle ABC with AB = BC. There is a regular hexagon PQRSTU. There is a circle with center O. There is a line segment AD. There is a line segment BE. There is a line segment CF. Line AD is perpendicular to line BE. Line BE is the angle bisector of angle ABC. The circle is the circumcircle of triangle ABC. Line CF is a diameter of the circle. Further, the inradius of triangle ABC equals the inradius of regular hexagon PQRSTU.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, O, P, Q, R, S, T, U = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"O\", \"P\", \"Q\", \"R\", \"S\", \"T\", \"U\"])\n\ntriangleABC = scene.add.isosceles_triangle(A, B, C)\nhexagonPQRSTU = scene.add.regular_hexagon(P, Q, R, S, T, U)\ncircleO = scene.add.circle(O)\nlineAD = scene.add.line_segment(A, D)\nlineBE = scene.add.line_segment(B, E)\nlineCF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.perpendicular(lineAD, lineBE)\nscene.relate.angle_bisector(A, B, C, lineBE)\nscene.relate.is_circumcircle(circleO, triangleABC)\nscene.relate.is_diameter(lineCF, circleO)\n\n### Extra relationships\n\nscene.constraint.eq(triangleABC.inradius, hexagonPQRSTU.inradius)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "isosceles_triangle(A, B, C)", "hexagonPQRSTU": "regular_hexagon(P, Q, R, S, T, U)", "circleO": "circle(O)", "lineAD": "line_segment(A, D)", "lineBE": "line_segment(B, E)", "lineCF": "line_segment(C, F)"}, "Rels": ["perpendicular(lineAD, lineBE)", "angle_bisector(A, B, C, lineBE)", "is_circumcircle(circleO, triangleABC)", "is_diameter(lineCF, circleO)"], "Points": ["A", "B", "C", "D", "E", "F", "O", "P", "Q", "R", "S", "T", "U"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangleABC').inradius, scene.get_object('hexagonPQRSTU').inradius)"], "possible_solution": {"points": {"A": [0.6001165794437691, -1.3853522862847685], "B": [-2.099489762829259, 0.09901352145255432], "C": [0.03895654621646099, 2.316729734170372], "D": [0.9043454402764425, -3.392408557533508], "E": [2.2239274508869014, 0.7543555190899532], "F": [-0.4024903858171001, -1.5373284606808892], "O": [-0.18176702371920248, 0.3897005831258301], "P": [-5.314478476056205, -7.906557214446068], "Q": [-6.235988654180929, -7.36692282940365], "R": [-7.164080829445617, -7.895156860984374], "S": [-7.170662826585584, -8.963025277607516], "T": [-6.249152648460861, -9.502659662649934], "U": [-5.321060473196172, -8.974425631069211]}, "circles": {"O": 1.9396288840056324}}}
{"unique_id": "3obj_4rel_1extra_gen0132", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M. There is a rhomboid ABCD. There is a parallelogram EFGH. There is a quadrilateral IJKL. There is a line segment AC. There is a line segment EG. There is a line segment IK. There is a line segment JL. There is a line segment BD. There is a line segment FH. Line AC and line EG intersect at M. M is the centroid of quadrilateral IJKL. Line BD is perpendicular to line FH. Line AC is parallel to line IK. Further, the length of line BD equals the length of line FH. Further, the length of line AC is less than or equal to the length of line EG. Further, the angle BAD measures 60 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K, L, M = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"L\", \"M\"])\n\nrhomboid1 = scene.add.rhomboid(A, B, C, D)\nparallelogram1 = scene.add.parallelogram(E, F, G, H)\nquadrilateral1 = scene.add.quadrilateral(I, J, K, L)\nline_AC = scene.add.line_segment(A, C)\nline_EG = scene.add.line_segment(E, G)\nline_IK = scene.add.line_segment(I, K)\nline_JL = scene.add.line_segment(J, L)\nline_BD = scene.add.line_segment(B, D)\nline_FH = scene.add.line_segment(F, H)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line_AC, line_EG, M)\nscene.relate.is_centroid(M, quadrilateral1)\nscene.relate.perpendicular(line_BD, line_FH)\nscene.relate.parallel(line_AC, line_IK)\n\n### Extra relationships\n\nscene.constraint.eq(line_BD.length, line_FH.length)\nscene.constraint.leq(line_AC.length, line_EG.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 60)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rhomboid1": "rhomboid(A, B, C, D)", "parallelogram1": "parallelogram(E, F, G, H)", "quadrilateral1": "quadrilateral(I, J, K, L)", "line_AC": "line_segment(A, C)", "line_EG": "line_segment(E, G)", "line_IK": "line_segment(I, K)", "line_JL": "line_segment(J, L)", "line_BD": "line_segment(B, D)", "line_FH": "line_segment(F, H)"}, "Rels": ["line_extensions_intersect_at(line_AC, line_EG, M)", "is_centroid(M, quadrilateral1)", "perpendicular(line_BD, line_FH)", "parallel(line_AC, line_IK)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_BD').length, scene.get_object('line_FH').length)", "scene.constraint.leq(scene.get_object('line_AC').length, scene.get_object('line_EG').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('A'), scene.get_object('D')), 60)"], "possible_solution": {"points": {"A": [-1.8700419936582375, 0.8704373797433793], "B": [0.8015709840978579, 3.620627340561812], "C": [3.2601059930946032, 2.9999032214384287], "D": [0.5884945279935972, 0.2497160566936209], "E": [4.84195032238253, -0.04611561988930622], "F": [3.130054007128132, 0.9713198272025945], "G": [-1.9527318461629093, 2.2018254774804125], "H": [-0.2408484479059204, 1.1843949699571656], "I": [-7.100758783779626, 0.6643395430506016], "J": [8.226172357445424, -1.036750818710042], "K": [-8.610778355778528, 0.03754662002625577], "L": [6.997986206568529, 6.7192576297204445], "M": [-0.12183788801349382, 1.5960970710885465]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0151", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a circle with center A. There is a circle with center B. There is a semicircle with center C and endpoints D and E. There is a line segment AC. There is a line segment BE. There is a line segment CD. There is a line segment DE. Line AC intersects line BE at point F. The extensions of line CD and line DE intersect at point G. Line CD is a diameter of the circle with center A. Line BE is a radius of the circle with center B.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ncircle1 = scene.add.circle(A)\ncircle2 = scene.add.circle(B)\nsemicircle1 = scene.add.semicircle(C, D, E)\nline_AC = scene.add.line_segment(A, C)\nline_BE = scene.add.line_segment(B, E)\nline_CD = scene.add.line_segment(C, D)\nline_DE = scene.add.line_segment(D, E)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_BE, F)\nscene.relate.line_extensions_intersect_at(line_CD, line_DE, G)\nscene.relate.is_diameter(line_CD, circle1)\nscene.relate.is_radius(line_BE, circle2)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "circle2": "circle(B)", "semicircle1": "semicircle(C, D, E)", "line_AC": "line_segment(A, C)", "line_BE": "line_segment(B, E)", "line_CD": "line_segment(C, D)", "line_DE": "line_segment(D, E)"}, "Rels": ["lines_intersect_at(line_AC, line_BE, F)", "line_extensions_intersect_at(line_CD, line_DE, G)", "is_diameter(line_CD, circle1)", "is_radius(line_BE, circle2)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [-1.2264851741997898, -3.425361649028738], "B": [-1.5328710391549616, -3.6433446469446373], "C": [-0.6752391574618399, -3.0331476606328738], "D": [-1.7777330933740607, -3.8175710782382812], "E": [0.4272559017875114, -2.2487232190356186], "F": [-1.0573575919786202, -3.3050190894159566], "G": [-0.8936699999228501, -3.1885618354842276]}, "circles": {"A": 0.6765375964078086, "B": 2.4056326594578175}}}
{"unique_id": "3obj_4rel_1extra_gen0177", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is an equilateral triangle ABC. There is an equilateral triangle DEF. There is a right trapezoid GHIJ. There are line segments AC, DF, GI, and HJ. Line AC and line DF intersect at point K. Point K lies on line AC. Triangle ABC and triangle DEF are mirror images across line GI. Line GI is perpendicular to line HJ. Further, the area of triangle ABC equals the area of trapezoid GHIJ.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\"])\n\ntriangle1 = scene.add.equilateral_triangle(A, B, C)\ntriangle2 = scene.add.equilateral_triangle(D, E, F)\ntrapezoid1 = scene.add.right_trapezoid(G, H, I, J)\nline_AC = scene.add.line_segment(A, C)\nline_DF = scene.add.line_segment(D, F)\nline_GI = scene.add.line_segment(G, I)\nline_HJ = scene.add.line_segment(H, J)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line_AC, line_DF, K)\nscene.relate.point_lies_on(K, line_AC)\nscene.relate.mirror_across_line(triangle1, triangle2, line_GI)\nscene.relate.perpendicular(line_GI, line_HJ)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.area, trapezoid1.area)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "equilateral_triangle(A, B, C)", "triangle2": "equilateral_triangle(D, E, F)", "trapezoid1": "right_trapezoid(G, H, I, J)", "line_AC": "line_segment(A, C)", "line_DF": "line_segment(D, F)", "line_GI": "line_segment(G, I)", "line_HJ": "line_segment(H, J)"}, "Rels": ["line_extensions_intersect_at(line_AC, line_DF, K)", "point_lies_on(K, line_AC)", "mirror_across_line(triangle1, triangle2, line_GI)", "perpendicular(line_GI, line_HJ)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('trapezoid1').area)"], "possible_solution": {"points": {"A": [-0.49726270468066114, 1.0837587919113627], "B": [0.045947562143245635, 1.603424695426374], "C": [-0.6757013006122972, 1.8140255890884995], "D": [-0.5640334318638788, 1.3570212484854114], "E": [0.15761504749160946, 1.1464223906242936], "F": [-0.3855935331001683, 0.6267552868296716], "G": [-1.302780327120244, 1.0317204079462368], "H": [-1.1027082475692283, 0.9911853261423533], "I": [-0.31173742131455745, 1.2738806775041833], "J": [-1.2165792727524107, 1.4572003913839686], "K": [-0.6145375700707678, 1.5637116568367202]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0182", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a circle with center A. There is an isosceles triangle with vertices B, C, D. There is a circle with center E. There is a line segment BC. There is a line segment DE. There is a line segment CD. The circle with center A is the circumcircle of the triangle BCD. Line DE is the angle bisector of angle BDC. Line DE is a radius of the circle with center E. Line BC is a diameter of the circle with center A.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ncircle1 = scene.add.circle(A)\nisosceles_triangle1 = scene.add.isosceles_triangle(B, C, D)\ncircle2 = scene.add.circle(E)\nline_BC = scene.add.line_segment(B, C)\nline_DE = scene.add.line_segment(D, E)\nline_CD = scene.add.line_segment(C, D)\n\n### relationships\n\nscene.relate.is_circumcircle(circle1, isosceles_triangle1)\nscene.relate.angle_bisector(B, D, C, line_DE)\nscene.relate.is_radius(line_DE, circle2)\nscene.relate.is_diameter(line_BC, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "isosceles_triangle1": "isosceles_triangle(B, C, D)", "circle2": "circle(E)", "line_BC": "line_segment(B, C)", "line_DE": "line_segment(D, E)", "line_CD": "line_segment(C, D)"}, "Rels": ["is_circumcircle(circle1, isosceles_triangle1)", "angle_bisector(B, D, C, line_DE)", "is_radius(line_DE, circle2)", "is_diameter(line_BC, circle1)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": [], "possible_solution": {"points": {"A": [1.369997615496852, -2.2968921025596236], "B": [0.34915552088458074, 2.914643348202768], "C": [2.3908439856592905, -7.508432600716341], "D": [0.15390755500655898, 2.8725734072060103], "E": [3.5303402785439233, 0.6932720661316597]}, "circles": {"A": 5.310584868293305, "E": 4.018663691259117}}}
{"unique_id": "3obj_4rel_1extra_gen0196", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, O, M. There is an obtuse triangle ABC with vertices A, B, C. There is a triangle DEF with vertices D, E, F. There is a circle with center O. There is a line AD. There is a line BE. There is a line CF. There is a line OM. M is the centroid of triangle ABC. line BE is the angle bisector of ∠ABC. line AD is an altitude of triangle ABC from vertex A. circle O is the circumcircle of triangle ABC. Further, the area of triangle ABC is twice the area of triangle DEF and the length of line BE is less than or equal to the circumradius of triangle ABC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, O, M = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"O\", \"M\"])\n\ntriangleABC = scene.add.obtuse_triangle(A, B, C)\ntriangleDEF = scene.add.triangle(D, E, F)\ncircleO = scene.add.circle(O)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_OM = scene.add.line_segment(O, M)\n\n### relationships\n\nscene.relate.is_centroid(M, triangleABC)\nscene.relate.angle_bisector(A, B, C, line_BE)\nscene.relate.is_altitude(line_AD, triangleABC, A)\nscene.relate.is_circumcircle(circleO, triangleABC)\n\n### Extra relationships\n\nscene.constraint.eq(triangleABC.area, 2 * triangleDEF.area)\nscene.constraint.leq(line_BE.length, triangleABC.circumradius)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "obtuse_triangle(A, B, C)", "triangleDEF": "triangle(D, E, F)", "circleO": "circle(O)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_OM": "line_segment(O, M)"}, "Rels": ["is_centroid(M, triangleABC)", "angle_bisector(A, B, C, line_BE)", "is_altitude(line_AD, triangleABC, A)", "is_circumcircle(circleO, triangleABC)"], "Points": ["A", "B", "C", "D", "E", "F", "O", "M"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangleABC').area, 2 * scene.get_object('triangleDEF').area)", "scene.constraint.leq(scene.get_object('line_BE').length, scene.get_object('triangleABC').circumradius)"], "possible_solution": {"points": {"A": [1.2890606894879315, -5.8351237833277], "B": [-2.481857035928636, 2.686361911429467], "C": [2.37822967139314, 3.5920938435973757], "D": [-0.37228115748059404, 3.0795064050317236], "E": [1.5333662331062488, 0.5705794914704977], "F": [-5.842172662486648, -1.4815376811794105], "O": [0.7182066523016856, -0.9926437156769137], "M": [0.39514535724991573, 0.14777827273235786]}, "circles": {"O": 4.876012281607931}}}
{"unique_id": "3obj_4rel_1extra_gen0200", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a circle with center A. There is a minor arc BC. There is an isosceles trapezoid DEFG. There is a line segment BE. There is a line segment CF. There is a line segment DE. There is a line segment GF. The angle BAC is acute. Line BE is a chord of the circle. Line BE is perpendicular to line CF. Line DE is a diameter of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ncircle1 = scene.add.circle(A)\nminor_arc1 = scene.add.minor_arc(A, B, C)\nisosceles_trapezoid1 = scene.add.isosceles_trapezoid(D, E, F, G)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_DE = scene.add.line_segment(D, E)\nline_GF = scene.add.line_segment(G, F)\n\n### relationships\n\nscene.relate.acute_angle(B, A, C)\nscene.relate.is_chord(line_BE, circle1)\nscene.relate.perpendicular(line_BE, line_CF)\nscene.relate.is_diameter(line_DE, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "minor_arc1": "minor_arc(A, B, C)", "isosceles_trapezoid1": "isosceles_trapezoid(D, E, F, G)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_DE": "line_segment(D, E)", "line_GF": "line_segment(G, F)"}, "Rels": ["acute_angle(B, A, C)", "is_chord(line_BE, circle1)", "perpendicular(line_BE, line_CF)", "is_diameter(line_DE, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [1.4306729028923373, -3.0159399235080717], "B": [-0.18602234766340223, -2.888312473144456], "C": [0.4360921000342802, -4.296877411286849], "D": [2.3503612403349714, -4.351666714810272], "E": [0.510984708710375, -1.6802132202938975], "F": [2.1323425126286755, -5.27552094916733], "G": [-0.4298531968457811, -1.5542672544558276]}, "circles": {"A": 1.6217250792351467}}}
{"unique_id": "3obj_4rel_1extra_gen0208", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a right triangle ABC. There is a right trapezoid DEFG. There is a scalene triangle HIJ. There is a line segment AC. There is a line segment DF. There is a line segment BI. Line AC intersects line DF at point K. Line AC is parallel to line DF. Line BI is an altitude of triangle ABC from vertex B. Angle JIH is obtuse. Further, the area of triangle ABC is equal to the area of triangle HIJ and the area of trapezoid DEFG is less than or equal to 12 square units.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\"])\n\ntriangle1 = scene.add.right_triangle(A, B, C)\ntrapezoid1 = scene.add.right_trapezoid(D, E, F, G)\ntriangle2 = scene.add.scalene_triangle(H, I, J)\nline_AC = scene.add.line_segment(A, C)\nline_DF = scene.add.line_segment(D, F)\nline_BI = scene.add.line_segment(B, I)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_DF, K)\nscene.relate.parallel(line_AC, line_DF)\nscene.relate.is_altitude(line_BI, triangle1, B)\nscene.relate.obtuse_angle(J, I, H)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.area, triangle2.area)\nscene.constraint.leq(trapezoid1.area, 12.0)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "right_triangle(A, B, C)", "trapezoid1": "right_trapezoid(D, E, F, G)", "triangle2": "scalene_triangle(H, I, J)", "line_AC": "line_segment(A, C)", "line_DF": "line_segment(D, F)", "line_BI": "line_segment(B, I)"}, "Rels": ["lines_intersect_at(line_AC, line_DF, K)", "parallel(line_AC, line_DF)", "is_altitude(line_BI, triangle1, B)", "obtuse_angle(J, I, H)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('triangle2').area)", "scene.constraint.leq(scene.get_object('trapezoid1').area, 12.0)"], "possible_solution": {"points": {"A": [0.29694333955264374, 1.3891676911077457], "B": [-1.6320209500338634, 0.2934643329212681], "C": [-0.8208706097855417, -1.1345500737395522], "D": [-0.14452572374520337, 0.3924519041772772], "E": [-0.7239089000662723, 0.37776601540160554], "F": [-1.1217075390688074, -1.8137573909386941], "G": [-0.08926765184860926, -1.7875879555312586], "H": [5.246568157832572, -5.674400595266255], "I": [-0.4251377198748615, -0.24109273196491035], "J": [-2.094490861443499, 2.000468943016318], "K": [-0.6240584974094342, -0.6902022433868263]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0223", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a regular pentagon with vertices A, B, C, D, E. There is a square with vertices F, G, H, I. There is a circle with center J. There is a line segment AC. There is a line segment FG. There is a line segment JH. Line AC intersects line FG at point K. The angle AKF is acute. Circle with center J is the circumcircle of the regular pentagon with vertices A, B, C, D, E. Line segment JH is a radius of the circle with center J. Further, the area of the circle with center J equals the perimeter of the square with vertices F, G, H, I.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\"])\n\npentagon1 = scene.add.regular_pentagon(A, B, C, D, E)\nsquare1 = scene.add.square(F, G, H, I)\ncircle1 = scene.add.circle(J)\nline_AC = scene.add.line_segment(A, C)\nline_FG = scene.add.line_segment(F, G)\nline_JH = scene.add.line_segment(J, H)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_FG, K)\nscene.relate.acute_angle(A, K, F)\nscene.relate.is_circumcircle(circle1, pentagon1)\nscene.relate.is_radius(line_JH, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(circle1.area, square1.perimeter)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"pentagon1": "regular_pentagon(A, B, C, D, E)", "square1": "square(F, G, H, I)", "circle1": "circle(J)", "line_AC": "line_segment(A, C)", "line_FG": "line_segment(F, G)", "line_JH": "line_segment(J, H)"}, "Rels": ["lines_intersect_at(line_AC, line_FG, K)", "acute_angle(A, K, F)", "is_circumcircle(circle1, pentagon1)", "is_radius(line_JH, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K"], "extra_rel": ["scene.constraint.eq(scene.get_object('circle1').area, scene.get_object('square1').perimeter)"], "possible_solution": {"points": {"A": [3.1364590881059975, 0.631680452248376], "B": [1.9541714859580657, 0.7494053545274547], "C": [1.4768614892128202, -0.33863797816494234], "D": [2.3641552902020884, -1.128810641280632], "E": [3.3898430139657867, -0.5291208713747517], "F": [2.7236248363781104, 0.15680906106359457], "G": [2.3157868382627194, 0.8476922624700041], "H": [1.6249018420887207, 0.4398552094460736], "I": [2.0327395532384225, -0.25102944116212866], "J": [2.46429354372611, -0.12309763877695207], "K": [2.621153224330174, 0.3303942903353812]}, "circles": {"J": 1.0106894271360156}}}
{"unique_id": "3obj_4rel_1extra_gen0233", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M. There is an isosceles triangle ABC. There is a regular hexagon with vertices D, E, F, G, H, I. There is a trapezoid JKLM. There is a line segment AB. There is a line segment BC. There is a line segment CD. There is a line segment DE. There is a line segment EF. There is a line segment FG. There is a line segment GH. There is a line segment HI. There is a line segment IJ. There is a line segment JK. There is a line segment KL. There is a line segment LM. There is a line segment MJ. There is a line segment AC. There is a line segment AM. There is a line segment BM. There is a line segment AL. There is a line segment BL. There is a line segment CM. There is a line segment CL. There is a line KL. There is a right angle at B between BA and BC. line AB is parallel to line KL. line BL is an altitude of triangle ABC from vertex B. line BL is a median of triangle ABC from vertex B.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K, L, M = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"L\", \"M\"])\n\ntriangle_ABC = scene.add.isosceles_triangle(A, B, C)\nhexagon_DEF_GHIJKL = scene.add.regular_hexagon(D, E, F, G, H, I)\ntrapezoid_JKLM = scene.add.trapezoid(J, K, L, M)\nline_AB = scene.add.line_segment(A, B)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_DE = scene.add.line_segment(D, E)\nline_EF = scene.add.line_segment(E, F)\nline_FG = scene.add.line_segment(F, G)\nline_GH = scene.add.line_segment(G, H)\nline_HI = scene.add.line_segment(H, I)\nline_IJ = scene.add.line_segment(I, J)\nline_JK = scene.add.line_segment(J, K)\nline_KL = scene.add.line_segment(K, L)\nline_LM = scene.add.line_segment(L, M)\nline_MJ = scene.add.line_segment(M, J)\nline_AC = scene.add.line_segment(A, C)\nline_AM = scene.add.line_segment(A, M)\nline_BM = scene.add.line_segment(B, M)\nline_AL = scene.add.line_segment(A, L)\nline_BL = scene.add.line_segment(B, L)\nline_CM = scene.add.line_segment(C, M)\nline_CL = scene.add.line_segment(C, L)\nline_KL_parallel_line = scene.add.line(K, L)\n\n### relationships\n\nscene.relate.right_angle(A, B, C)\nscene.relate.parallel(line_AB, line_KL_parallel_line)\nscene.relate.is_altitude(line_BL, triangle_ABC, B)\nscene.relate.is_median(line_BL, triangle_ABC, B)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle_ABC": "isosceles_triangle(A, B, C)", "hexagon_DEF_GHIJKL": "regular_hexagon(D, E, F, G, H, I)", "trapezoid_JKLM": "trapezoid(J, K, L, M)", "line_AB": "line_segment(A, B)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_DE": "line_segment(D, E)", "line_EF": "line_segment(E, F)", "line_FG": "line_segment(F, G)", "line_GH": "line_segment(G, H)", "line_HI": "line_segment(H, I)", "line_IJ": "line_segment(I, J)", "line_JK": "line_segment(J, K)", "line_KL": "line_segment(K, L)", "line_LM": "line_segment(L, M)", "line_MJ": "line_segment(M, J)", "line_AC": "line_segment(A, C)", "line_AM": "line_segment(A, M)", "line_BM": "line_segment(B, M)", "line_AL": "line_segment(A, L)", "line_BL": "line_segment(B, L)", "line_CM": "line_segment(C, M)", "line_CL": "line_segment(C, L)", "line_KL_parallel_line": "line(K, L)"}, "Rels": ["right_angle(A, B, C)", "parallel(line_AB, line_KL_parallel_line)", "is_altitude(line_BL, triangle_ABC, B)", "is_median(line_BL, triangle_ABC, B)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M"], "extra_rel": [], "possible_solution": {"points": {"A": [1.0403363780404868, -1.5733421143911583], "B": [1.2536101795553474, -1.3627715558807136], "C": [1.043039634816643, -1.1494977164490248], "D": [-2.7229463451314944, -0.9630056482258817], "E": [-3.9560801421437604, -7.130997078715697], "F": [0.7689902284790064, -11.28291798843839], "G": [6.727194396114039, -9.266847467671269], "H": [7.960328193126305, -3.098856037181453], "I": [3.2352578225035384, 1.0530648725412404], "J": [2.2055306907185934, -0.9174030311163132], "K": [2.6778903544138464, 0.25404346462763805], "L": [1.0416880067543184, -1.3614199379659517], "M": [2.015280554424987, 1.0530782842680688]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0234", "nl_description": "Diagram description: The diagram contains points A, B, C, D, O. There is a triangle ABC. There is a rhomboid ABCD. There is a circle with center O. There is a line segment AC. There is a line segment BD. There is a line segment AD. There is a line segment BC. The extensions of line AC and line BD intersect at point O. The extension of line AD intersects the circle at points A and D. Line BC is an altitude of triangle ABC from vertex B. Line AC is a diameter of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, O = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"O\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\nrhomboidABCD = scene.add.rhomboid(A, B, C, D)\ncircleO = scene.add.circle(O)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_AD = scene.add.line_segment(A, D)\nline_BC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line_AC, line_BD, O)\nscene.relate.line_extension_intersects_circle_at(line_AD, circleO, A, D)\nscene.relate.is_altitude(line_BC, triangleABC, B)\nscene.relate.is_diameter(line_AC, circleO)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "rhomboidABCD": "rhomboid(A, B, C, D)", "circleO": "circle(O)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_AD": "line_segment(A, D)", "line_BC": "line_segment(B, C)"}, "Rels": ["line_extensions_intersect_at(line_AC, line_BD, O)", "line_extension_intersects_circle_at(line_AD, circleO, A, D)", "is_altitude(line_BC, triangleABC, B)", "is_diameter(line_AC, circleO)"], "Points": ["A", "B", "C", "D", "O"], "extra_rel": [], "possible_solution": {"points": {"A": [0.417580664904518, 3.2121694199859436], "B": [-5.161398958334657, -4.104361330677326], "C": [-4.999826289760523, -4.222344281189524], "D": [0.5766289488218307, 3.090897658972138], "O": [-2.2911124529237403, -0.5050948342755864]}, "circles": {"O": 4.599464970492526}}}
{"unique_id": "3obj_4rel_1extra_gen0248", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a kite B, C, D, E. There is an equilateral triangle F, G, H. There is a line segment BD. There is a line segment CF. There is a line segment GE. There is a line segment HF. The extension of line BD intersects the circle at points B and D. C is the orthocenter of triangle FGH. Line CF is a chord of the circle. Line CF is perpendicular to line GE. Further, the area of triangle FGH equals the area of the circle and the slope of line HF is less than or equal to 0.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ncircle1 = scene.add.circle(A)\nkite1 = scene.add.kite(B, C, D, E)\ntriangle1 = scene.add.equilateral_triangle(F, G, H)\nline_BD = scene.add.line_segment(B, D)\nline_CF = scene.add.line_segment(C, F)\nline_GE = scene.add.line_segment(G, E)\nline_HF = scene.add.line_segment(H, F)\n\n### relationships\n\nscene.relate.line_extension_intersects_circle_at(line_BD, circle1, B, D)\nscene.relate.is_orthocenter(C, triangle1)\nscene.relate.is_chord(line_CF, circle1)\nscene.relate.perpendicular(line_CF, line_GE)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.area, circle1.area)\nscene.constraint.leq(line_HF.slope, 0)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "kite1": "kite(B, C, D, E)", "triangle1": "equilateral_triangle(F, G, H)", "line_BD": "line_segment(B, D)", "line_CF": "line_segment(C, F)", "line_GE": "line_segment(G, E)", "line_HF": "line_segment(H, F)"}, "Rels": ["line_extension_intersects_circle_at(line_BD, circle1, B, D)", "is_orthocenter(C, triangle1)", "is_chord(line_CF, circle1)", "perpendicular(line_CF, line_GE)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('circle1').area)", "scene.constraint.leq(scene.get_object('line_HF').slope, 0)"], "possible_solution": {"points": {"A": [-1.3564170553755062, 0.29813281435912886], "B": [-0.569741538187937, 0.4061155157785554], "C": [-1.7830398077001364, -0.3715774664129646], "D": [-1.5910626877508351, 1.0567232123474528], "E": [-2.2096622642842685, -1.0412895494984913], "F": [-0.6122765242101051, 0.02105269674334251], "G": [-2.028393382617376, -1.5818041217695864], "H": [-2.708449265424667, 0.4460172545647355]}, "circles": {"A": 0.7940520942719544}}}
{"unique_id": "3obj_4rel_1extra_gen0256", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, M. There is a square with points A, B, C, D. There is a square with points E, F, G, H. There is a major arc with center I, start point J, and end point K. There is a line segment AC. There is a line segment EG. There is a line segment IK. The squares ABCD and EFGH are congruent. The extensions of line segment AC and line segment EG intersect at point M. Square ABCD is the mirror image of square EFGH across line IK. Line segment AC is perpendicular to line segment EG. Further, the area of square ABCD equals four times the radius of the major arc.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K, M = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"M\"])\n\nsquare1 = scene.add.square(A, B, C, D)\nsquare2 = scene.add.square(E, F, G, H)\nsemicircle1 = scene.add.major_arc(I, J, K)\nline_AC = scene.add.line_segment(A, C)\nline_EG = scene.add.line_segment(E, G)\nline_IK = scene.add.line_segment(I, K)\n\n### relationships\n\nscene.relate.congruent(square1, square2)\nscene.relate.line_extensions_intersect_at(line_AC, line_EG, M)\nscene.relate.mirror_across_line(square1, square2, line_IK)\nscene.relate.perpendicular(line_AC, line_EG)\n\n### Extra relationships\n\nscene.constraint.eq(square1.area, 4 * semicircle1.radius)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"square1": "square(A, B, C, D)", "square2": "square(E, F, G, H)", "semicircle1": "major_arc(I, J, K)", "line_AC": "line_segment(A, C)", "line_EG": "line_segment(E, G)", "line_IK": "line_segment(I, K)"}, "Rels": ["congruent(square1, square2)", "line_extensions_intersect_at(line_AC, line_EG, M)", "mirror_across_line(square1, square2, line_IK)", "perpendicular(line_AC, line_EG)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "M"], "extra_rel": ["scene.constraint.eq(scene.get_object('square1').area, 4 * scene.get_object('semicircle1').radius)"], "possible_solution": {"points": {"A": [1.647563921875744, 2.683266234088159], "B": [-2.4758861098962437, 2.379190217630962], "C": [-2.171811775844043, -1.744262467990849], "D": [1.9516376385333383, -1.4401864739629373], "E": [-2.676552151183082, 2.364391779622528], "F": [1.4468971703531714, 2.6684684219257107], "G": [1.7509759056649288, -1.454984301140244], "H": [-2.3724731502420005, -1.7590606541480032], "I": [-0.15039826480082316, -2.413568452415557], "J": [-1.3337192999682288, 1.6931741730571543], "K": [-0.46470815964607287, 1.8486846780857424], "M": [-0.3550578836192148, 0.3617711021435204]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0260", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a circle with center A. There is a square BCDE. There is a regular pentagon FGHIJ. There is a line segment AB. There is a line segment AC. There is a line segment BD. There is a line segment FG. The circle is the circumcircle of the square BCDE. Line BD is a diameter of the circle. Line AB is a radius of the circle. Line AB is perpendicular to line AC. Further, the area of the circle equals the product of the square's inradius and the pentagon's perimeter.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\"])\n\ncircle1 = scene.add.circle(A)\nsquare1 = scene.add.square(B, C, D, E)\npentagon1 = scene.add.regular_pentagon(F, G, H, I, J)\nline_AB = scene.add.line_segment(A, B)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_FG = scene.add.line_segment(F, G)\n\n### relationships\n\nscene.relate.is_circumcircle(circle1, square1)\nscene.relate.perpendicular(line_AB, line_AC)\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.is_radius(line_AB, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(circle1.area, square1.inradius * pentagon1.perimeter)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "square1": "square(B, C, D, E)", "pentagon1": "regular_pentagon(F, G, H, I, J)", "line_AB": "line_segment(A, B)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_FG": "line_segment(F, G)"}, "Rels": ["is_circumcircle(circle1, square1)", "perpendicular(line_AB, line_AC)", "is_diameter(line_BD, circle1)", "is_radius(line_AB, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J"], "extra_rel": ["scene.constraint.eq(scene.get_object('circle1').area, scene.get_object('square1').inradius * scene.get_object('pentagon1').perimeter)"], "possible_solution": {"points": {"A": [0.0790898755514022, 0.7281360420497243], "B": [-0.12007787098670264, 1.4376309008903638], "C": [0.788584689399231, 0.9273038603263961], "D": [0.27825757825640113, 0.018641367030207027], "E": [-0.6304050051010401, 0.5289684256396532], "F": [-2.4087220847438826, 2.239818028344332], "G": [-2.023834732832697, 1.7100660357557498], "H": [-1.4010739156004572, 1.9124132913166056], "I": [-1.401073915600457, 2.567222765372058], "J": [-2.023834732832697, 2.769570020932914]}, "circles": {"A": 0.7369196830144471}}}
{"unique_id": "3obj_4rel_1extra_gen0267", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is an isosceles triangle ABC. There is a right triangle DEF. There is a circle with center G. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment DE. There is an acute angle at B in triangle ABC. Line AD is an altitude of triangle ABC from vertex A. Line DE is a chord of the circle with center G. Line BE is perpendicular to line CF. Further, the inradius of triangle ABC equals the inradius of triangle DEF and the slope of line AD is less than or equal to 1.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntriangle1 = scene.add.isosceles_triangle(A, B, C)\ntriangle2 = scene.add.right_triangle(D, E, F)\ncircle1 = scene.add.circle(G)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_DE = scene.add.line_segment(D, E)\n\n### relationships\n\nscene.relate.acute_angle(A, B, C)\nscene.relate.is_altitude(line_AD, triangle1, A)\nscene.relate.is_chord(line_DE, circle1)\nscene.relate.perpendicular(line_BE, line_CF)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.inradius, triangle2.inradius)\nscene.constraint.leq(line_AD.slope, 1.0)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "isosceles_triangle(A, B, C)", "triangle2": "right_triangle(D, E, F)", "circle1": "circle(G)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_DE": "line_segment(D, E)"}, "Rels": ["acute_angle(A, B, C)", "is_altitude(line_AD, triangle1, A)", "is_chord(line_DE, circle1)", "perpendicular(line_BE, line_CF)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').inradius, scene.get_object('triangle2').inradius)", "scene.constraint.leq(scene.get_object('line_AD').slope, 1.0)"], "possible_solution": {"points": {"A": [1.4694586379943027, -1.0858970325889141], "B": [1.0181228718481166, -1.8906880824392978], "C": [0.8687688961596358, -0.9801460771533017], "D": [0.901398509956039, -1.1790743043862817], "E": [1.0622349813461927, -1.694000817996068], "F": [2.3116549930398955, -1.3037464789302697], "G": [1.0767124065525475, -1.40689765341981]}, "circles": {"G": 0.2874676031022621}}}
{"unique_id": "3obj_4rel_1extra_gen0268", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a triangle ABC. There is a circle with center D. There is a circle with center E. There is a line segment AD. There is a line segment BE. There is a line segment CD. The circle with center D is the circumcircle of triangle ABC. Line BE is the perpendicular bisector of line AD. Line CD is a chord of the circle with center E. Line AD is a radius of the circle with center D. Further, the perimeter of triangle ABC equals twice the area of the circle with center D divided by the circumradius of triangle ABC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ntriangle1 = scene.add.triangle(A, B, C)\ncircle1 = scene.add.circle(D)\ncircle2 = scene.add.circle(E)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CD = scene.add.line_segment(C, D)\n\n### relationships\n\nscene.relate.is_circumcircle(circle1, triangle1)\nscene.relate.perpendicular_bisector_at(line_AD, line_BE)\nscene.relate.is_chord(line_CD, circle2)\nscene.relate.is_radius(line_AD, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.perimeter, 2 * circle1.area / triangle1.circumradius)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "triangle(A, B, C)", "circle1": "circle(D)", "circle2": "circle(E)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CD": "line_segment(C, D)"}, "Rels": ["is_circumcircle(circle1, triangle1)", "perpendicular_bisector_at(line_AD, line_BE)", "is_chord(line_CD, circle2)", "is_radius(line_AD, circle1)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').perimeter, 2 * scene.get_object('circle1').area / scene.get_object('triangle1').circumradius)"], "possible_solution": {"points": {"A": [0.15372771366070911, -0.17544466380061408], "B": [0.4105113368454573, -0.060739463532862595], "C": [0.45715905660551015, -0.39969422092226436], "D": [0.33575317969493174, -0.24390735966340726], "E": [0.2600780882865582, -0.43104065852889023]}, "circles": {"D": 0.1770690101348751, "E": 0.2007114579794166}}}
{"unique_id": "3obj_4rel_1extra_gen0271", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a triangle ABC. There is an equilateral triangle DEF. There is a circle with center G. There is a line AD. There is a line BE. There is a line CF. There is a line DE. line AD is an altitude of triangle ABC from vertex A. line BE is an altitude of triangle ABC from vertex B. line AD and line BE intersect at point H. circle with center G is the circumcircle of triangle ABC. Further, the inradius of triangle ABC equals one-sixth of the perimeter of equilateral triangle DEF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangle1 = scene.add.triangle(A, B, C)\nequilateral_triangle1 = scene.add.equilateral_triangle(D, E, F)\ncircle1 = scene.add.circle(G)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_DE = scene.add.line_segment(D, E)\n\n### relationships\n\nscene.relate.is_altitude(line_AD, triangle1, A)\nscene.relate.is_altitude(line_BE, triangle1, B)\nscene.relate.lines_intersect_at(line_AD, line_BE, H)\nscene.relate.is_circumcircle(circle1, triangle1)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.inradius, equilateral_triangle1.perimeter / 6)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "triangle(A, B, C)", "equilateral_triangle1": "equilateral_triangle(D, E, F)", "circle1": "circle(G)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_DE": "line_segment(D, E)"}, "Rels": ["is_altitude(line_AD, triangle1, A)", "is_altitude(line_BE, triangle1, B)", "lines_intersect_at(line_AD, line_BE, H)", "is_circumcircle(circle1, triangle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').inradius, scene.get_object('equilateral_triangle1').perimeter / 6)"], "possible_solution": {"points": {"A": [-0.7412046446945392, -3.083731043713833], "B": [-1.6825982958921586, -2.4310610987119494], "C": [-0.6169969606128449, -1.7216055753144255], "D": [-1.3314078365616449, -2.1972464352249], "E": [-0.6899433465435538, -2.521578410081954], "F": [-1.2915557485693554, -2.914936541862306], "G": [-0.9489110807943313, -2.378067054107747], "H": [-1.1429783684845898, -2.4802671539667416]}, "circles": {"G": 0.7355992671819325}}}
{"unique_id": "3obj_4rel_1extra_gen0281", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a square with vertices A, B, C, D. There is a circle with center E. There is an isosceles triangle with vertices F, G, H. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment FG. Line segment AC is a chord of the circle. Line segment AC and line segment BD intersect at point E. Line segment EF is a radius of the circle. Line segment FG is an altitude of the isosceles triangle from vertex F. Further, length of line AC is equal to 2 times the length of line EF. Further, area of the isosceles triangle is equal to 1/2 times the square of the length of line FG.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\nsquare1 = scene.add.square(A, B, C, D)\ncircle1 = scene.add.circle(E)\ntriangle1 = scene.add.isosceles_triangle(F, G, H)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\nline_FG = scene.add.line_segment(F, G)\n\n### relationships\n\nscene.relate.is_chord(line_AC, circle1)\nscene.relate.lines_intersect_at(line_AC, line_BD, E)\nscene.relate.is_radius(line_EF, circle1)\nscene.relate.is_altitude(line_FG, triangle1, F)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, 2 * line_EF.length)\nscene.constraint.eq(triangle1.area, (1/2) * line_FG.length * line_FG.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"square1": "square(A, B, C, D)", "circle1": "circle(E)", "triangle1": "isosceles_triangle(F, G, H)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)", "line_FG": "line_segment(F, G)"}, "Rels": ["is_chord(line_AC, circle1)", "lines_intersect_at(line_AC, line_BD, E)", "is_radius(line_EF, circle1)", "is_altitude(line_FG, triangle1, F)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, 2 * scene.get_object('line_EF').length)", "scene.constraint.eq(scene.get_object('triangle1').area, (1/2) * scene.get_object('line_FG').length * scene.get_object('line_FG').length)"], "possible_solution": {"points": {"A": [-0.9306751596834643, -2.5704539657571472], "B": [-1.437079343813067, -1.7323431351214522], "C": [-0.598968576908043, -1.2259390632179883], "D": [-0.09256439068301972, -2.064049951140667], "E": [-0.7648219725822949, -1.898196252428665], "F": [-0.22659610944280073, -1.4625932850410686], "G": [-2.6343402994042773, 0.6761792280392306], "H": [-0.49556759900667957, 3.0839233442859406]}, "circles": {"E": 0.6924140606251271}}}
{"unique_id": "3obj_4rel_1extra_gen0288", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a kite with vertices A, B, C, D. There is a circle with center E. There is a parallelogram with vertices F, G, H, I. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment GH. Line AC is perpendicular to line BD. Line EF is a radius of the circle with center E. Line GH is parallel to line AC. Point A lies on the circle with center E. Further, the area of the kite equals the area of the parallelogram.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\nkite1 = scene.add.kite(A, B, C, D)\ncircle1 = scene.add.circle(E)\nparallelogram1 = scene.add.parallelogram(F, G, H, I)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\nline_GH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.is_radius(line_EF, circle1)\nscene.relate.parallel(line_GH, line_AC)\nscene.relate.point_lies_on(A, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(kite1.area, parallelogram1.area)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"kite1": "kite(A, B, C, D)", "circle1": "circle(E)", "parallelogram1": "parallelogram(F, G, H, I)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)", "line_GH": "line_segment(G, H)"}, "Rels": ["perpendicular(line_AC, line_BD)", "is_radius(line_EF, circle1)", "parallel(line_GH, line_AC)", "point_lies_on(A, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": ["scene.constraint.eq(scene.get_object('kite1').area, scene.get_object('parallelogram1').area)"], "possible_solution": {"points": {"A": [0.14047742586725714, 0.9105676322653091], "B": [0.8869341148431827, -1.6280305326744546], "C": [0.33578152219046536, 0.9600011144403375], "D": [0.5997942024666859, -0.4935849248222893], "E": [-0.6676974988277353, -0.8516097996025334], "F": [-2.6020701323824675, -0.9805238785428172], "G": [0.18698127567815295, -0.31344203802005066], "H": [3.2206248840476968, 0.4544054583970811], "I": [0.43157952993874465, -0.21267486783727438]}, "circles": {"E": 1.9386635368367888}}}
{"unique_id": "3obj_4rel_1extra_gen0296", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, K, L. There is a kite with points A, B, C, D. There is a trapezoid with points E, F, G, H. There is a circle with center I. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment GH. There is a line segment KL. Line AC is tangent to the circle at point A. The extension of line BD intersects the circle at points B and D. Line EF is a diameter of the circle. Line AC is perpendicular to line BD. Further, the length of line AC is equal to the length of line EF and the area of the circle is equal to 4π.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, K, L = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"K\", \"L\"])\n\nkite1 = scene.add.kite(A, B, C, D)\ntrapezoid1 = scene.add.trapezoid(E, F, G, H)\ncircle1 = scene.add.circle(I)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\nline_GH = scene.add.line_segment(G, H)\nline_KL = scene.add.line_segment(K, L)\n\n### relationships\n\nscene.relate.tangent_to_circle(line_AC, circle1, A)\nscene.relate.line_extension_intersects_circle_at(line_BD, circle1, B, D)\nscene.relate.is_diameter(line_EF, circle1)\nscene.relate.perpendicular(line_AC, line_BD)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_EF.length)\nscene.constraint.eq(circle1.area, 4 * 3.14159)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"kite1": "kite(A, B, C, D)", "trapezoid1": "trapezoid(E, F, G, H)", "circle1": "circle(I)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)", "line_GH": "line_segment(G, H)", "line_KL": "line_segment(K, L)"}, "Rels": ["tangent_to_circle(line_AC, circle1, A)", "line_extension_intersects_circle_at(line_BD, circle1, B, D)", "is_diameter(line_EF, circle1)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "K", "L"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_EF').length)", "scene.constraint.eq(scene.get_object('circle1').area, 4 * 3.14159)"], "possible_solution": {"points": {"A": [-0.14697110242529735, 0.4775277317178453], "B": [-2.82703594476977, 1.1239216404919008], "C": [-3.6091690590116428, -1.521237200202554], "D": [-2.9273328314468503, 1.2976655834157884], "E": [0.8148473407382442, 2.5969165484648267], "F": [-3.1091233094060513, 1.82204698772609], "G": [-1.5733864506623705, 0.49143489886355696], "H": [-1.8735121262027543, 0.4321689854398707], "I": [-1.1471379610442027, 2.209481709516527], "K": [-3.9461391410400912, 4.023142592740382], "L": [5.111945855310092, 8.180416403253114]}, "circles": {"I": 1.9999991525093774}}}
{"unique_id": "3obj_4rel_1extra_gen0305", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a minor arc with center A, start point B, and end point C. There is a rhomboid with vertices D, E, F, G. There is an isosceles triangle with vertices H, I, J. There are line segments DE, EF, FG, GD, HI, IJ, and HJ. Line DE is parallel to line FG. Line HI is an altitude of the isosceles triangle from vertex H. Point B lies on the minor arc. Point C lies on the minor arc. Further, the length of line HI is equal to the length of line IJ and the angle H I J is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\"])\n\narc1 = scene.add.minor_arc(A, B, C)\nrhomboid1 = scene.add.rhomboid(D, E, F, G)\ntriangle1 = scene.add.isosceles_triangle(H, I, J)\nline_DE = scene.add.line_segment(D, E)\nline_EF = scene.add.line_segment(E, F)\nline_FG = scene.add.line_segment(F, G)\nline_GD = scene.add.line_segment(G, D)\nline_HI = scene.add.line_segment(H, I)\nline_IJ = scene.add.line_segment(I, J)\nline_HJ = scene.add.line_segment(H, J)\n\n### relationships\n\nscene.relate.parallel(line_DE, line_FG)\nscene.relate.is_altitude(line_HI, triangle1, H)\nscene.relate.point_lies_on(B, arc1)\nscene.relate.point_lies_on(C, arc1)\n\n### Extra relationships\n\nscene.constraint.eq(line_HI.length, line_IJ.length)\nscene.constraint.eq(scene.angle(scene.get_object('H'), scene.get_object('I'), scene.get_object('J')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"arc1": "minor_arc(A, B, C)", "rhomboid1": "rhomboid(D, E, F, G)", "triangle1": "isosceles_triangle(H, I, J)", "line_DE": "line_segment(D, E)", "line_EF": "line_segment(E, F)", "line_FG": "line_segment(F, G)", "line_GD": "line_segment(G, D)", "line_HI": "line_segment(H, I)", "line_IJ": "line_segment(I, J)", "line_HJ": "line_segment(H, J)"}, "Rels": ["parallel(line_DE, line_FG)", "is_altitude(line_HI, triangle1, H)", "point_lies_on(B, arc1)", "point_lies_on(C, arc1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_HI').length, scene.get_object('line_IJ').length)", "scene.constraint.eq(scene.angle(scene.get_object('H'), scene.get_object('I'), scene.get_object('J')), 90)"], "possible_solution": {"points": {"A": [7.53850549148554, 6.3416784309294165], "B": [5.1589265868198115, -5.055566459836523], "C": [-4.103914431340061, 6.458491219551444], "D": [-8.390525060706727, -5.836047611401109], "E": [-2.8247248132049005, 0.2130560595421433], "F": [4.163530282310276, 0.5362813414378309], "G": [-1.4022699643182042, -5.512822328595374], "H": [6.80183924869385, -9.999948391439531], "I": [4.66339795128129, 4.519104472006941], "J": [-9.855654919954018, 2.380663175040057]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0307", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J.\nThere is a regular pentagon ABCDE.\nThere is a rhombus FGHI.\nThere is a circle with center J.\nThere is a line segment AC.\nThere is a line segment FH.\nThere is a line segment JG.\nPoint G lies on the circle.\nPoint H lies on the circle.\nThe circle is the circumcircle of the pentagon.\nLine JG is a radius of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\"])\n\npentagon1 = scene.add.regular_pentagon(A, B, C, D, E)\nrhombus1 = scene.add.rhombus(F, G, H, I)\ncircle1 = scene.add.circle(J)\nline_AC = scene.add.line_segment(A, C)\nline_FH = scene.add.line_segment(F, H)\nline_JG = scene.add.line_segment(J, G)\n\n### relationships\n\nscene.relate.point_lies_on(G, circle1)\nscene.relate.point_lies_on(H, circle1)\nscene.relate.is_circumcircle(circle1, pentagon1)\nscene.relate.is_radius(line_JG, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"pentagon1": "regular_pentagon(A, B, C, D, E)", "rhombus1": "rhombus(F, G, H, I)", "circle1": "circle(J)", "line_AC": "line_segment(A, C)", "line_FH": "line_segment(F, H)", "line_JG": "line_segment(J, G)"}, "Rels": ["point_lies_on(G, circle1)", "point_lies_on(H, circle1)", "is_circumcircle(circle1, pentagon1)", "is_radius(line_JG, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J"], "extra_rel": [], "possible_solution": {"points": {"A": [-6.223954294390792, 2.2507946805340575], "B": [-4.5854883966713125, -0.006467828264531342], "C": [-1.9323903715905446, 0.8542733645047745], "D": [-1.9311515143248883, 3.6435031859519196], "E": [-4.58348388350827, 4.506600825271749], "F": [-4.433243319618206, 0.33874168413617134], "G": [-4.033632607338139, -0.11590336143511731], "H": [-3.429116585216596, -0.0850581757640108], "I": [-3.8287273636911534, 0.3695868584289048], "J": [-3.851293524884458, 2.249740567438294]}, "circles": {"J": 2.372660677936633}}}
{"unique_id": "3obj_4rel_1extra_gen0310", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is an isosceles triangle ABC. There is an isosceles trapezoid ABCD. There is a right trapezoid EFGH. There is a line segment AD. There is a line segment BC. There is a line segment EF. There is a line segment GH. F is the orthocenter of triangle ABC. F lies on line AD. Line AD is perpendicular to line BC. Line EF is parallel to line GH.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangleABC = scene.add.isosceles_triangle(A, B, C)\ntrapezoidABCD = scene.add.isosceles_trapezoid(A, B, C, D)\ntrapezoidEFGH = scene.add.right_trapezoid(E, F, G, H)\nline_AD = scene.add.line_segment(A, D)\nline_BC = scene.add.line_segment(B, C)\nline_EF = scene.add.line_segment(E, F)\nline_GH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.is_orthocenter(F, triangleABC)\nscene.relate.point_lies_on(F, line_AD)\nscene.relate.perpendicular(line_AD, line_BC)\nscene.relate.parallel(line_EF, line_GH)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "isosceles_triangle(A, B, C)", "trapezoidABCD": "isosceles_trapezoid(A, B, C, D)", "trapezoidEFGH": "right_trapezoid(E, F, G, H)", "line_AD": "line_segment(A, D)", "line_BC": "line_segment(B, C)", "line_EF": "line_segment(E, F)", "line_GH": "line_segment(G, H)"}, "Rels": ["is_orthocenter(F, triangleABC)", "point_lies_on(F, line_AD)", "perpendicular(line_AD, line_BC)", "parallel(line_EF, line_GH)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.6208516650726096, 0.54517421961446], "B": [0.3402105320089832, -0.6776710910174448], "C": [0.5253191563611315, 0.8665849673228742], "D": [0.9234042156099725, 0.3600655356359259], "E": [-0.4267774499893579, 1.8891928964331663], "F": [0.018799728458601735, 0.46849967893439604], "G": [0.4491389908864667, 0.6760810342448387], "H": [0.02429585817341117, 2.0306647989519506]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0311", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is an equilateral triangle ABC. There is a circle with center D. There is a square EFGH. There is a line segment AD. There is a line segment BD. There is a line segment CD. There is a line segment EF. There is a line segment FG. Point A lies on the circle. Point B lies on the circle. Point C lies on the circle. The circle is the circumcircle of triangle ABC. Further, the length of line AD is equal to the length of line BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangle1 = scene.add.equilateral_triangle(A, B, C)\ncircle1 = scene.add.circle(D)\nsquare1 = scene.add.square(E, F, G, H)\nline_AD = scene.add.line_segment(A, D)\nline_BD = scene.add.line_segment(B, D)\nline_CD = scene.add.line_segment(C, D)\nline_EF = scene.add.line_segment(E, F)\nline_FG = scene.add.line_segment(F, G)\n\n### relationships\n\nscene.relate.point_lies_on(A, circle1)\nscene.relate.point_lies_on(B, circle1)\nscene.relate.point_lies_on(C, circle1)\nscene.relate.is_circumcircle(circle1, triangle1)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BD.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "equilateral_triangle(A, B, C)", "circle1": "circle(D)", "square1": "square(E, F, G, H)", "line_AD": "line_segment(A, D)", "line_BD": "line_segment(B, D)", "line_CD": "line_segment(C, D)", "line_EF": "line_segment(E, F)", "line_FG": "line_segment(F, G)"}, "Rels": ["point_lies_on(A, circle1)", "point_lies_on(B, circle1)", "point_lies_on(C, circle1)", "is_circumcircle(circle1, triangle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BD').length)"], "possible_solution": {"points": {"A": [2.14110899340298, 2.0563344670224963], "B": [1.4850575094516987, 2.6111688537474524], "C": [1.332582556757994, 1.7655944956226637], "D": [1.6529165071337917, 2.1443660414571433], "E": [-1.5754126083646696, -0.3706078423240725], "F": [-1.4387048301639553, -0.5271860443722718], "G": [-1.2821263357667037, -0.3904786337127517], "H": [-1.4188340464779807, -0.23390022213031314]}, "circles": {"D": 0.49606609710414235}}}
{"unique_id": "3obj_4rel_1extra_gen0314", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K.\nThere is a quadrilateral ABCD.\nThere is a major arc with points E, F, G.\nThere is a rectangle HIJK.\nThere is a line segment AC.\nThere is a line segment BD.\nThere is a line segment EF.\nQuadrilateral ABCD is congruent to rectangle HIJK.\nThere is an acute angle at vertex B of quadrilateral ABCD.\nLine AC is perpendicular to line BD.\nQuadrilateral ABCD is a mirror image of rectangle HIJK across line EF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\"])\n\nquad1 = scene.add.quadrilateral(A, B, C, D)\nsemicircle1 = scene.add.major_arc(E, F, G)\nrect1 = scene.add.rectangle(H, I, J, K)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.congruent(quad1, rect1)\nscene.relate.acute_angle(A, B, C)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.mirror_across_line(quad1, rect1, line_EF)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"quad1": "Quadrilateral(A, B, C, D)", "semicircle1": "MajorArc(E, F, G)", "rect1": "Rectangle(H, I, J, K)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["congruent(quad1, rect1)", "acute_angle(A, B, C)", "perpendicular(line_AC, line_BD)", "mirror_across_line(quad1, rect1, line_EF)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K"], "extra_rel": [], "possible_solution": {"points": {"A": [-2.455020618022123, 2.3974794803678843], "B": [3.9392857273857773, 2.7653787819379105], "C": [4.307183427984834, -3.6289277358966894], "D": [-2.087122347791512, -3.996826269476213], "E": [3.7023186130798216, 2.058173199299649], "F": [-1.5337977137451846, -3.2867590244890272], "G": [-3.745259021530482, 2.7784525301055147], "H": [4.168189091355986, -4.090880834796597], "I": [4.404503068527182, 2.309639238816626], "J": [-1.9960172528795097, 2.5459521167620847], "K": [-2.232330678681127, -3.854567499291304]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0319", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a rhombus ABCD. There is a rhombus HIJK. There is a right isosceles triangle EFG. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment FG. There is a line segment EG. There is a line segment HI. There is a line segment IJ. Line AC is perpendicular to line BD. F is the orthocenter of triangle EFG. Rhombus HIJK is the mirror image of rhombus ABCD across line EG. Line EF is parallel to line IJ. Further, the area of rhombus ABCD equals the area of triangle EFG. Further, the length of line AC is less than or equal to twice the length of line EF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\"])\n\nrhombus1 = scene.add.rhombus(A, B, C, D)\ntriangle1 = scene.add.right_isosceles_triangle(E, F, G)\nrhombus2 = scene.add.rhombus(H, I, J, K)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\nline_FG = scene.add.line_segment(F, G)\nline_EG = scene.add.line_segment(E, G)\nline_HI = scene.add.line_segment(H, I)\nline_IJ = scene.add.line_segment(I, J)\n\n### relationships\n\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.is_orthocenter(F, triangle1)\nscene.relate.mirror_across_line(rhombus1, rhombus2, line_EG)\nscene.relate.parallel(line_EF, line_IJ)\n\n### Extra relationships\n\nscene.constraint.eq(rhombus1.area, triangle1.area)\nscene.constraint.leq(line_AC.length, 2 * line_EF.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rhombus1": "rhombus(A, B, C, D)", "triangle1": "right_isosceles_triangle(E, F, G)", "rhombus2": "rhombus(H, I, J, K)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)", "line_FG": "line_segment(F, G)", "line_EG": "line_segment(E, G)", "line_HI": "line_segment(H, I)", "line_IJ": "line_segment(I, J)"}, "Rels": ["perpendicular(line_AC, line_BD)", "is_orthocenter(F, triangle1)", "mirror_across_line(rhombus1, rhombus2, line_EG)", "parallel(line_EF, line_IJ)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K"], "extra_rel": ["scene.constraint.eq(scene.get_object('rhombus1').area, scene.get_object('triangle1').area)", "scene.constraint.leq(scene.get_object('line_AC').length, 2 * scene.get_object('line_EF').length)"], "possible_solution": {"points": {"A": [0.49205091986212357, -1.754031817507883], "B": [0.81070380821961, -1.6229074258954388], "C": [0.9473858039338904, -1.3066004868735783], "D": [0.6287331070619261, -1.4377235277670408], "E": [1.5861346984889253, -1.487038163199575], "F": [1.2124216250590334, -1.325548631818285], "G": [1.0509323723595163, -1.6992612188171354], "H": [0.6063888771223346, -2.0423779883061433], "I": [0.9283087732648623, -1.9194959608408435], "J": [1.2446160559151145, -2.0561799890273234], "K": [0.922695267332438, -2.1790629918451376]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0328", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, M. There is a square ABCD. There is a rhombus EFGH. There is an isosceles triangle IJK. There is a line segment AC. There is a line segment EG. There is a line segment IJ. There is a line segment JK. There is a line segment KI. The extensions of line segment AC and line segment EG intersect at point M. Point M lies on line segment AC. Point M lies on line segment EG. Line segment IJ is rotated 90 degrees counterclockwise around point J to form line segment JK. Further, the area of triangle IJK equals half the area of square ABCD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K, M = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"M\"])\n\nsquare1 = scene.add.square(A, B, C, D)\nrhombus1 = scene.add.rhombus(E, F, G, H)\ntriangle1 = scene.add.isosceles_triangle(I, J, K)\nline_AC = scene.add.line_segment(A, C)\nline_EG = scene.add.line_segment(E, G)\nline_IJ = scene.add.line_segment(I, J)\nline_JK = scene.add.line_segment(J, K)\nline_KI = scene.add.line_segment(K, I)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line_AC, line_EG, M)\nscene.relate.point_lies_on(M, line_AC)\nscene.relate.point_lies_on(M, line_EG)\nscene.relate.rotation_around_point(line_IJ, line_JK, J, 90)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.area, square1.area / 2)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"square1": "square(A, B, C, D)", "rhombus1": "rhombus(E, F, G, H)", "triangle1": "isosceles_triangle(I, J, K)", "line_AC": "line_segment(A, C)", "line_EG": "line_segment(E, G)", "line_IJ": "line_segment(I, J)", "line_JK": "line_segment(J, K)", "line_KI": "line_segment(K, I)"}, "Rels": ["line_extensions_intersect_at(line_AC, line_EG, M)", "point_lies_on(M, line_AC)", "point_lies_on(M, line_EG)", "rotation_around_point(line_IJ, line_JK, J, 90)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "M"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').area, scene.get_object('square1').area / 2)"], "possible_solution": {"points": {"A": [-1.7071007042932718, 1.1585271312848373], "B": [-1.0245780740093131, 0.2626492272390952], "C": [-1.9204560828496824, -0.41987328059012896], "D": [-2.6029785510754238, 0.4760047228245585], "E": [-1.8319295324150426, 0.6655506797111483], "F": [-1.3216663770588004, 0.05692193734624113], "G": [-1.7144144119781122, -0.6334016097834049], "H": [-2.2246777798393262, -0.024772872864065435], "I": [0.6208436911054799, 3.6518432978134037], "J": [1.7443165391954905, 3.5728301685846424], "K": [1.8233296509707275, 4.696302946137465], "M": [-1.808597688148757, 0.4076532482566594]}, "circles": {}}}
{"unique_id": "3obj_4rel_1extra_gen0332", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a right trapezoid ABCD. There is a parallelogram EFGH. There is a circle with center I. There is a line segment AB. There is a line segment BC. There is a line segment CD. There is a line segment DA. There is a line segment EF. There is a line segment FG. There is a line segment GH. There is a line segment HE. trapezoid ABCD is similar to parallelogram EFGH. J is the midpoint of line AB. line AB is perpendicular to line BC. line BC is tangent to the circle at point B.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\"])\n\ntrapezoid1 = scene.add.right_trapezoid(A, B, C, D)\nparallelogram1 = scene.add.parallelogram(E, F, G, H)\ncircle1 = scene.add.circle(I)\nline_AB = scene.add.line_segment(A, B)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_DA = scene.add.line_segment(D, A)\nline_EF = scene.add.line_segment(E, F)\nline_FG = scene.add.line_segment(F, G)\nline_GH = scene.add.line_segment(G, H)\nline_HE = scene.add.line_segment(H, E)\n\n### relationships\n\nscene.relate.similar(trapezoid1, parallelogram1)\nscene.relate.is_midpoint(J, line_AB)\nscene.relate.perpendicular(line_AB, line_BC)\nscene.relate.tangent_to_circle(line_BC, circle1, B)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "right_trapezoid(A, B, C, D)", "parallelogram1": "parallelogram(E, F, G, H)", "circle1": "circle(I)", "line_AB": "line_segment(A, B)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_DA": "line_segment(D, A)", "line_EF": "line_segment(E, F)", "line_FG": "line_segment(F, G)", "line_GH": "line_segment(G, H)", "line_HE": "line_segment(H, E)"}, "Rels": ["similar(trapezoid1, parallelogram1)", "is_midpoint(J, line_AB)", "perpendicular(line_AB, line_BC)", "tangent_to_circle(line_BC, circle1, B)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.5816594850878664, 0.5582544809970632], "B": [1.28693306928317, 0.3703373374914601], "C": [1.5370208920346495, 2.8571445236370625], "D": [-0.3315846261619334, 3.0450787253217406], "E": [0.6960989104631035, 3.580212420036587], "F": [-1.0818333301271779, 4.251706657033114], "G": [-1.9754876855484782, 1.8855543802630403], "H": [-0.19754684725325122, 1.2140397920302508], "I": [1.5235380536048204, 0.3465177791004606], "J": [0.35269569462183437, 0.46431549538994077]}, "circles": {"I": 0.2379330234980827}}}
{"unique_id": "3obj_4rel_1extra_gen0335", "nl_description": "Diagram description: The diagram contains points A, B, C, O, H, M, D, E, F. There is a triangle with points A, B, C. There is a circle with center O. There is an equilateral triangle with points D, E, F. There is a line segment AH. There is a line segment BM. Line AH is an altitude of triangle ABC from vertex A. H is the orthocenter of triangle ABC. The circle with center O is the circumcircle of triangle ABC. Line BM is a median of triangle ABC from vertex B.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O, H, M, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"O\", \"H\", \"M\", \"D\", \"E\", \"F\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\ncircleO = scene.add.circle(O)\nequilateral_triangleDEF = scene.add.equilateral_triangle(D, E, F)\nline_altitude = scene.add.line_segment(A, H)\nline_median = scene.add.line_segment(B, M)\n\n### relationships\n\nscene.relate.is_altitude(line_altitude, triangleABC, A)\nscene.relate.is_orthocenter(H, triangleABC)\nscene.relate.is_circumcircle(circleO, triangleABC)\nscene.relate.is_median(line_median, triangleABC, B)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "circleO": "circle(O)", "equilateral_triangleDEF": "equilateral_triangle(D, E, F)", "line_altitude": "line_segment(A, H)", "line_median": "line_segment(B, M)"}, "Rels": ["is_altitude(line_altitude, triangleABC, A)", "is_orthocenter(H, triangleABC)", "is_circumcircle(circleO, triangleABC)", "is_median(line_median, triangleABC, B)"], "Points": ["A", "B", "C", "O", "H", "M", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [9.85490030448456, 9.460907034895465], "B": [-5.215555346298036, -2.2082884106002956], "C": [-5.570971824884469, -1.7289780649627806], "O": [2.2585898542047693, 3.7051581879834248], "H": [-5.450390733272563, -1.8883020545970612], "M": [2.141892602557101, 3.866094078992226], "D": [3.140132384597329, 7.8882444121005175], "E": [-4.793093607359825, 3.1356647375149467], "F": [3.2893464985370353, -1.358458845955417]}, "circles": {"O": 9.530418210599946}}}
{"unique_id": "3obj_4rel_1extra_gen0342", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a circle with center A. There is a kite with vertices B, C, D, E. There is a rhombus with vertices F, G, H, I. There is a line segment BD. There is a line segment FH. There is a line segment AG. There is a line segment BF. Line BD and line FH intersect at point A. Line AG and line BF intersect at point C. Line BD is a diameter of the circle. Line AG is a radius of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\ncircle1 = scene.add.circle(A)\nkite1 = scene.add.kite(B, C, D, E)\nrhombus1 = scene.add.rhombus(F, G, H, I)\nline_BD = scene.add.line_segment(B, D)\nline_FH = scene.add.line_segment(F, H)\nline_AG = scene.add.line_segment(A, G)\nline_BF = scene.add.line_segment(B, F)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_BD, line_FH, A)\nscene.relate.lines_intersect_at(line_AG, line_BF, C)\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.is_radius(line_AG, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "kite1": "kite(B, C, D, E)", "rhombus1": "rhombus(F, G, H, I)", "line_BD": "line_segment(B, D)", "line_FH": "line_segment(F, H)", "line_AG": "line_segment(A, G)", "line_BF": "line_segment(B, F)"}, "Rels": ["lines_intersect_at(line_BD, line_FH, A)", "lines_intersect_at(line_AG, line_BF, C)", "is_diameter(line_BD, circle1)", "is_radius(line_AG, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": [], "possible_solution": {"points": {"A": [-1.183140993098817, -0.3190090149138747], "B": [-0.8212720184139706, 0.9152941402508323], "C": [-0.9910502455974869, -0.37532305256557413], "D": [-1.5450097585974143, -1.5533119166409837], "E": [7.562080285069581, -2.8829059533336747], "F": [-1.3515673387029086, -3.1158914637945254], "G": [0.05116209445780808, -0.6808768313884286], "H": [-1.0492202014398728, 1.9048757678854242], "I": [-2.451949311697024, -0.5301388706034649]}, "circles": {"A": 1.2862553674918011}}}
{"unique_id": "3obj_5rel_2extra_gen0001", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a circle with center A. There is a triangle BCD. There is a triangle EFG. There is a line segment BC. There is a line segment EF. There is a line segment BD. There is a line segment CF. Triangle BCD is similar to triangle EFG. Extensions of line BC and line EF intersect at H. Circle with center A is the circumcircle of triangle BCD. I is the orthocenter of triangle BCD. Line BD is perpendicular to line CF. Further, the circumradius of triangle BCD is constrained to be exactly 3 units, and the length of line BC is constrained to be less than or equal to 4 units.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\ncircle1 = scene.add.circle(A)\ntriangle1 = scene.add.triangle(B, C, D)\ntriangle2 = scene.add.triangle(E, F, G)\nline_BC = scene.add.line_segment(B, C)\nline_EF = scene.add.line_segment(E, F)\nline_BD = scene.add.line_segment(B, D)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.similar(triangle1, triangle2)\nscene.relate.line_extensions_intersect_at(line_BC, line_EF, H)\nscene.relate.is_circumcircle(circle1, triangle1)\nscene.relate.is_orthocenter(I, triangle1)\nscene.relate.perpendicular(line_BD, line_CF)\n\n### Extra relationships\n\nscene.constraint.eq(triangle1.circumradius, 3.0)\nscene.constraint.leq(line_BC.length, 4.0)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "triangle1": "triangle(B, C, D)", "triangle2": "triangle(E, F, G)", "line_BC": "line_segment(B, C)", "line_EF": "line_segment(E, F)", "line_BD": "line_segment(B, D)", "line_CF": "line_segment(C, F)"}, "Rels": ["similar(triangle1, triangle2)", "line_extensions_intersect_at(line_BC, line_EF, H)", "is_circumcircle(circle1, triangle1)", "is_orthocenter(I, triangle1)", "perpendicular(line_BD, line_CF)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": ["scene.constraint.eq(scene.get_object('triangle1').circumradius, 3.0)", "scene.constraint.leq(scene.get_object('line_BC').length, 4.0)"], "possible_solution": {"points": {"A": [4.299115812837089, -1.7906626127065086], "B": [1.8200187514788564, -3.480010276585866], "C": [1.3039987947951777, -1.6200707258421434], "D": [4.873057486771182, 1.15395167516827], "E": [-5.372811803118464, 3.383390547867057], "F": [-6.416408199103839, 3.466445007309135], "G": [-7.525657682540857, 1.2799996581871713], "H": [0.03520564649416697, 2.9530244967010333], "I": [-0.6012684863457424, -0.36478371438462714]}, "circles": {"A": 2.9999542414304106}}}
{"unique_id": "3obj_5rel_2extra_gen0003", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L. There is a quadrilateral with vertices A, B, C, D. There is an equilateral triangle with vertices E, F, G. There is an equilateral triangle with vertices H, I, J. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment HI. The equilateral triangle with vertices E, F, G is the mirror image of the equilateral triangle with vertices H, I, J across line AC. Line AC intersects line BD at point K. Line AC is perpendicular to line BD. The extensions of line EF and line HI intersect at point L. Point K is the centroid of the quadrilateral with vertices A, B, C, D.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K, L = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"L\"])\n\nquad1 = scene.add.quadrilateral(A, B, C, D)\ntri1 = scene.add.equilateral_triangle(E, F, G)\ntri2 = scene.add.equilateral_triangle(H, I, J)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\nline_HI = scene.add.line_segment(H, I)\n\n### relationships\n\nscene.relate.mirror_across_line(tri1, tri2, line_AC)\nscene.relate.lines_intersect_at(line_AC, line_BD, K)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.line_extensions_intersect_at(line_EF, line_HI, L)\nscene.relate.is_centroid(K, quad1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"quad1": "quadrilateral(A, B, C, D)", "tri1": "equilateral_triangle(E, F, G)", "tri2": "equilateral_triangle(H, I, J)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)", "line_HI": "line_segment(H, I)"}, "Rels": ["mirror_across_line(tri1, tri2, line_AC)", "lines_intersect_at(line_AC, line_BD, K)", "perpendicular(line_AC, line_BD)", "line_extensions_intersect_at(line_EF, line_HI, L)", "is_centroid(K, quad1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L"], "extra_rel": [], "possible_solution": {"points": {"A": [0.8061497293635127, 1.114670761094365], "B": [0.6519857388451937, 0.1320640843741579], "C": [-0.3397036688827, 0.20831729784924802], "D": [-0.185558718720406, 1.1909266424525493], "E": [-0.12432627856731535, -0.043929342164748364], "F": [0.3757949115062587, -0.1487722229004066], "G": [0.2165306855894781, 0.33676454276667345], "H": [-0.5355768442992864, 0.4759917479988523], "I": [-0.522436573907569, 0.9868150031744807], "J": [-0.08662332144312715, 0.7200233291340536], "K": [0.23321890679900767, 0.6614908066094061], "L": [-0.5466727301234483, 0.04460867981602205]}, "circles": {}}}
{"unique_id": "3obj_5rel_2extra_gen0017", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a rectangle with points A, B, C, D. There is a rhombus with points E, F, G, H. There is a circle with center I. There is a line segment AC. There is a line segment EG. There is a line segment IF. Line AC is a diameter of the circle. Line IF is a radius of the circle. Line AC is perpendicular to line EG. The circle is the circumcircle of the rectangle. Point F lies on the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\nrhombus1 = scene.add.rhombus(E, F, G, H)\ncircle1 = scene.add.circle(I)\nline_AC = scene.add.line_segment(A, C)\nline_EG = scene.add.line_segment(E, G)\nline_IF = scene.add.line_segment(I, F)\n\n### relationships\n\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.is_radius(line_IF, circle1)\nscene.relate.perpendicular(line_AC, line_EG)\nscene.relate.is_circumcircle(circle1, rectangle1)\nscene.relate.point_lies_on(F, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "rhombus1": "rhombus(E, F, G, H)", "circle1": "circle(I)", "line_AC": "line_segment(A, C)", "line_EG": "line_segment(E, G)", "line_IF": "line_segment(I, F)"}, "Rels": ["is_diameter(line_AC, circle1)", "is_radius(line_IF, circle1)", "perpendicular(line_AC, line_EG)", "is_circumcircle(circle1, rectangle1)", "point_lies_on(F, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": [], "possible_solution": {"points": {"A": [-1.0037557048382693, 0.029187090459683186], "B": [-0.8509022278523422, -0.9618778554541585], "C": [1.1377479285438308, -0.6551654098949039], "D": [0.9848945622144031, 0.33589915033241685], "E": [0.1709304047263048, 1.0162399649439309], "F": [0.927683989826486, -1.0360455471110808], "G": [-0.8789702851155523, -2.2691522045937695], "H": [-1.6357236791003764, -0.216866812783763], "I": [0.06699617375314247, -0.3129890640985152]}, "circles": {"I": 1.1240969998050652}}}
{"unique_id": "3obj_5rel_2extra_gen0021", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, O. There is a triangle ABC. There is a circle with center O. There is a right triangle DEF. There is a line segment AD. There is a line segment BE. There is a line segment CF. Triangle ABC has a circumcircle centered at O. Line AD is tangent to the circle at A. Line BE intersects the circle at points B and G. Line CF is an altitude of triangle ABC from vertex C to side AB. Line BE is a median of triangle ABC from vertex B to the midpoint of side AC. Further, the inradius of right triangle DEF equals the inradius of triangle ABC. Further, angle AOB measures 60 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, O = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"O\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\ncircleO = scene.add.circle(O)\nright_triangleDEF = scene.add.right_triangle(D, E, F)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_circumcircle(circleO, triangleABC)\nscene.relate.tangent_to_circle(line_AD, circleO, A)\nscene.relate.line_extension_intersects_circle_at(line_BE, circleO, B, G)\nscene.relate.is_altitude(line_CF, triangleABC, C)\nscene.relate.is_median(line_BE, triangleABC, B)\n\n### Extra relationships\n\nscene.constraint.eq(right_triangleDEF.inradius, triangleABC.inradius)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('O'), scene.get_object('B')), 60)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "circleO": "circle(O)", "right_triangleDEF": "right_triangle(D, E, F)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)"}, "Rels": ["is_circumcircle(circleO, triangleABC)", "tangent_to_circle(line_AD, circleO, A)", "line_extension_intersects_circle_at(line_BE, circleO, B, G)", "is_altitude(line_CF, triangleABC, C)", "is_median(line_BE, triangleABC, B)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "O"], "extra_rel": ["scene.constraint.eq(scene.get_object('right_triangleDEF').inradius, scene.get_object('triangleABC').inradius)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('O'), scene.get_object('B')), 60)"], "possible_solution": {"points": {"A": [0.1664528817149733, 0.8137552555380805], "B": [-1.221579514877285, 1.8339641827408795], "C": [0.08479698918980731, -0.7324935570792037], "D": [-1.9870260235300699, 5.723205621438534], "E": [0.12565462876129402, 0.04060831019707856], "F": [0.8512756380209818, 0.3103793977973048], "G": [0.28613003262114556, -0.17300060420714594], "O": [-1.4110851986478106, 0.12178556094988138]}, "circles": {"O": 1.7226247600068534}}}
{"unique_id": "3obj_5rel_2extra_gen0032", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a regular heptagon ABCDEFG. There is a circle with center H. There is a right isosceles triangle IJK. There is a line segment HI. There is a line segment HJ. There is a line segment IK. There is a line segment JK. The circle is the incircle of the heptagon. The extensions of line HI and line HJ intersect at H. Line HI is a radius of the circle. Line HJ is a radius of the circle. Angle I H J is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\"])\n\nheptagon1 = scene.add.regular_heptagon(A, B, C, D, E, F, G)\ncircle1 = scene.add.circle(H)\ntriangle1 = scene.add.right_isosceles_triangle(I, J, K)\nline_HI = scene.add.line_segment(H, I)\nline_HJ = scene.add.line_segment(H, J)\nline_IK = scene.add.line_segment(I, K)\nline_JK = scene.add.line_segment(J, K)\n\n### relationships\n\nscene.relate.is_incircle(circle1, heptagon1)\nscene.relate.line_extensions_intersect_at(line_HI, line_HJ, H)\nscene.relate.is_radius(line_HI, circle1)\nscene.relate.is_radius(line_HJ, circle1)\nscene.relate.right_angle(I, H, J)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"heptagon1": "regular_heptagon(A, B, C, D, E, F, G)", "circle1": "circle(H)", "triangle1": "right_isosceles_triangle(I, J, K)", "line_HI": "line_segment(H, I)", "line_HJ": "line_segment(H, J)", "line_IK": "line_segment(I, K)", "line_JK": "line_segment(J, K)"}, "Rels": ["is_incircle(circle1, heptagon1)", "line_extensions_intersect_at(line_HI, line_HJ, H)", "is_radius(line_HI, circle1)", "is_radius(line_HJ, circle1)", "right_angle(I, H, J)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K"], "extra_rel": [], "possible_solution": {"points": {"A": [1.091020737678093, 4.7867727519837375], "B": [0.5456444523209119, 5.919258277711064], "C": [-0.6798049372278709, 6.198959104070966], "D": [-1.662539046026043, 5.415254803957359], "E": [-1.662539046026043, 4.158290700010116], "F": [-0.6798049372278709, 3.374586399896508], "G": [0.5456444523209119, 3.654287226256411], "H": [-0.3574825707846677, 4.786772729038759], "I": [-1.6088727501846232, 4.4163744783564525], "J": [0.012915548206660995, 3.535382488492119], "K": [-0.8680764594788835, 1.913594120150819]}, "circles": {"H": 1.305056418243205}}}
{"unique_id": "3obj_5rel_2extra_gen0035", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a right trapezoid ABCD. There is a rectangle EFGH. There is a circle with center I. There is a line segment AB. There is a line segment BC. There is a line segment CD. There is a line segment DA. There is a line segment EF. There is a line segment FG. There is a line segment GH. There is a line segment HE. There is a line segment AC. There is a line segment BD. There is a line segment EI. There is a line segment HI. line AC intersects the circle at points A and C. points A, I, and C are collinear. line AB is perpendicular to line BC. line AC is a diameter of the circle. line EI is a radius of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\ntrapezoid1 = scene.add.right_trapezoid(A, B, C, D)\nrectangle1 = scene.add.rectangle(E, F, G, H)\ncircle1 = scene.add.circle(I)\nline_AB = scene.add.line_segment(A, B)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_DA = scene.add.line_segment(D, A)\nline_EF = scene.add.line_segment(E, F)\nline_FG = scene.add.line_segment(F, G)\nline_GH = scene.add.line_segment(G, H)\nline_HE = scene.add.line_segment(H, E)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EI = scene.add.line_segment(E, I)\nline_HI = scene.add.line_segment(H, I)\n\n### relationships\n\nscene.relate.line_intersects_circle_at(line_AC, circle1, A, C)\nscene.relate.collinear(A, I, C)\nscene.relate.perpendicular(line_AB, line_BC)\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.is_radius(line_EI, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "right_trapezoid(A, B, C, D)", "rectangle1": "rectangle(E, F, G, H)", "circle1": "circle(I)", "line_AB": "line_segment(A, B)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_DA": "line_segment(D, A)", "line_EF": "line_segment(E, F)", "line_FG": "line_segment(F, G)", "line_GH": "line_segment(G, H)", "line_HE": "line_segment(H, E)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EI": "line_segment(E, I)", "line_HI": "line_segment(H, I)"}, "Rels": ["line_intersects_circle_at(line_AC, circle1, A, C)", "collinear(A, I, C)", "perpendicular(line_AB, line_BC)", "is_diameter(line_AC, circle1)", "is_radius(line_EI, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": [], "possible_solution": {"points": {"A": [0.46829970375876956, -0.11775404909790621], "B": [0.2191096153453253, -0.22859098287485935], "C": [0.4192189259892946, -0.6784854770875633], "D": [0.6684076797427078, -0.5676490492873365], "E": [0.1665833586572065, -0.446913647489546], "F": [0.0808195098882181, -0.08391141794560736], "G": [-0.29203014860836224, -0.17200149924582625], "H": [-0.2062661353057723, -0.5350045101188756], "I": [0.4437585941078845, -0.3981195691315175]}, "circles": {"I": 0.2814375335421658}}}
{"unique_id": "3obj_5rel_2extra_gen0042", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a parallelogram ABCD. There is an isosceles triangle EFG. There is a circle with center H. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment FG. There is a line segment EG. I is the midpoint of line AC. J is the midpoint of line BD. A, I, C are collinear. B, J, D are collinear. The circle is the circumcircle of triangle EFG.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\"])\n\nparallelogram1 = scene.add.parallelogram(A, B, C, D)\ntriangle1 = scene.add.isosceles_triangle(E, F, G)\ncircle1 = scene.add.circle(H)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\nline_FG = scene.add.line_segment(F, G)\nline_EG = scene.add.line_segment(E, G)\n\n### relationships\n\nscene.relate.is_midpoint(I, line_AC)\nscene.relate.is_midpoint(J, line_BD)\nscene.relate.collinear(A, I, C)\nscene.relate.collinear(B, J, D)\nscene.relate.is_circumcircle(circle1, triangle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"parallelogram1": "parallelogram(A, B, C, D)", "triangle1": "isosceles_triangle(E, F, G)", "circle1": "circle(H)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)", "line_FG": "line_segment(F, G)", "line_EG": "line_segment(E, G)"}, "Rels": ["is_midpoint(I, line_AC)", "is_midpoint(J, line_BD)", "collinear(A, I, C)", "collinear(B, J, D)", "is_circumcircle(circle1, triangle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J"], "extra_rel": [], "possible_solution": {"points": {"A": [-7.988745976072449, 7.713267035647428], "B": [-4.399691512373694, 4.638911693631588], "C": [7.335417400614646, -5.4018779942967], "D": [3.439118631276903, -2.0646128917838102], "E": [7.937884187740211, -6.900527533088904], "F": [2.8315209173942897, -6.838135628644629], "G": [5.961569455399254, -2.803103335713574], "H": [5.400208086713962, -5.599152556503247], "I": [-0.3266631278333511, 1.1556932101912152], "J": [-0.4802983095066853, 1.2871590005256353]}, "circles": {"H": 2.851912709267997}}}
{"unique_id": "3obj_5rel_2extra_gen0043", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a right trapezoid ABCD. There is a regular hexagon EFGHIJ. There is a circle with center K. There is a line AB. There is a line CD. There is a line KG. There is a line KH. The extended line AB intersects the circle at points A and B. Line AB is parallel to line CD. Line KG is a radius of the circle. Line KH is a radius of the circle. Lines KG and KH are perpendicular. Further, the perimeter of the hexagon is 12 and the area of the trapezoid is twice the area of the hexagon.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\"])\n\ntrapezoid1 = scene.add.right_trapezoid(A, B, C, D)\nhexagon1 = scene.add.regular_hexagon(E, F, G, H, I, J)\ncircle1 = scene.add.circle(K)\nline_AB = scene.add.line_segment(A, B)\nline_CD = scene.add.line_segment(C, D)\nline_KG = scene.add.line_segment(K, G)\nline_KH = scene.add.line_segment(K, H)\n\n### relationships\n\nscene.relate.line_extension_intersects_circle_at(line_AB, circle1, A, B)\nscene.relate.parallel(line_AB, line_CD)\nscene.relate.is_radius(line_KG, circle1)\nscene.relate.is_radius(line_KH, circle1)\nscene.relate.perpendicular(line_KG, line_KH)\n\n### Extra relationships\n\nscene.constraint.eq(hexagon1.perimeter, 12)\nscene.constraint.eq(trapezoid1.area, 2 * hexagon1.area)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "right_trapezoid(A, B, C, D)", "hexagon1": "regular_hexagon(E, F, G, H, I, J)", "circle1": "circle(K)", "line_AB": "line_segment(A, B)", "line_CD": "line_segment(C, D)", "line_KG": "line_segment(K, G)", "line_KH": "line_segment(K, H)"}, "Rels": ["line_extension_intersects_circle_at(line_AB, circle1, A, B)", "parallel(line_AB, line_CD)", "is_radius(line_KG, circle1)", "is_radius(line_KH, circle1)", "perpendicular(line_KG, line_KH)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K"], "extra_rel": ["scene.constraint.eq(scene.get_object('hexagon1').perimeter, 12)", "scene.constraint.eq(scene.get_object('trapezoid1').area, 2 * scene.get_object('hexagon1').area)"], "possible_solution": {"points": {"A": [-0.1721883577909395, -3.432410998505551], "B": [-2.808051497013108, -2.412229861384647], "C": [-2.322523099967571, 3.4827479748887034], "D": [1.8754011947603375, 1.8579886679184079], "E": [-0.2988881843068584, -0.4852753356782329], "F": [-2.2568827075226605, -0.8930221201890715], "G": [-2.882760895432756, -2.792568510020175], "H": [-1.5506445601270493, -4.28436811534044], "I": [0.4073499630887527, -3.876621330829602], "J": [1.0332281509988483, -1.977074940998498], "K": [-1.4708028426005215, -2.872410430955776]}, "circles": {"K": 1.4142134997376}}}
{"unique_id": "3obj_5rel_2extra_gen0044", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, M. There is a trapezoid ABCD. There is a rhombus EFGH. There is a rhombus IJKL. There is a line segment AC. There is a line segment BD. There is a line segment EG. There is a line segment FH. There is a line segment IK. There is a line segment JL. Line segment AC intersects line segment BD at point M. Point M is the midpoint of line segment AC. Point M is the midpoint of line segment BD. Rhombus IJKL is the mirror image of rhombus EFGH across line segment AC. Line segment AC is perpendicular to line segment BD. Further, the area of rhombus EFGH is equal to the area of rhombus IJKL. Further, angle AMB is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K, L, M = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"L\", \"M\"])\n\ntrapezoid1 = scene.add.trapezoid(A, B, C, D)\nrhombus1 = scene.add.rhombus(E, F, G, H)\nrhombus2 = scene.add.rhombus(I, J, K, L)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EG = scene.add.line_segment(E, G)\nline_FH = scene.add.line_segment(F, H)\nline_IK = scene.add.line_segment(I, K)\nline_JL = scene.add.line_segment(J, L)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_BD, M)\nscene.relate.is_midpoint(M, line_AC)\nscene.relate.is_midpoint(M, line_BD)\nscene.relate.mirror_across_line(rhombus1, rhombus2, line_AC)\nscene.relate.perpendicular(line_AC, line_BD)\n\n### Extra relationships\n\nscene.constraint.eq(rhombus1.area, rhombus2.area)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('M'), scene.get_object('B')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "trapezoid(A, B, C, D)", "rhombus1": "rhombus(E, F, G, H)", "rhombus2": "rhombus(I, J, K, L)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EG": "line_segment(E, G)", "line_FH": "line_segment(F, H)", "line_IK": "line_segment(I, K)", "line_JL": "line_segment(J, L)"}, "Rels": ["lines_intersect_at(line_AC, line_BD, M)", "is_midpoint(M, line_AC)", "is_midpoint(M, line_BD)", "mirror_across_line(rhombus1, rhombus2, line_AC)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M"], "extra_rel": ["scene.constraint.eq(scene.get_object('rhombus1').area, scene.get_object('rhombus2').area)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('M'), scene.get_object('B')), 90)"], "possible_solution": {"points": {"A": [-2.4828058166501696, 0.8595608919225545], "B": [-0.5443037191740675, 2.611508965978808], "C": [1.2707292815158364, 0.7319355232859395], "D": [-0.6677819281925971, -1.020025354472001], "E": [0.21592173211017365, 1.1662398183031712], "F": [-0.1041757936408121, 0.42899251243454883], "G": [-0.906537579523341, 0.4758839973099822], "H": [-0.5864426311087185, 1.213129290074852], "I": [0.18887553840074361, 0.3702906954328286], "J": [-0.08042452505147893, 1.127576146112906], "K": [-0.8841235055645303, 1.1352810981809667], "L": [-0.6148268819949806, 0.3779973587437381], "M": [-0.6060416745862944, 0.7957486539793521]}, "circles": {}}}
{"unique_id": "3obj_5rel_2extra_gen0045", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a square with vertices B, C, D, E. There is a major arc with center F, start point G, and end point H. There are line segments BC, CD, DE, EB, BD, and CF. Line BC intersects the circle at points B and C. Line BD is a diameter of the circle. Line BC is perpendicular to line CD. Point F lies on the circle. Point G lies on the circle. Further, the length of line BC is equal to the length of line CD and the angle BCD is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ncircle1 = scene.add.circle(A)\nsquare1 = scene.add.square(B, C, D, E)\nsemicircle1 = scene.add.major_arc(F, G, H)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_DE = scene.add.line_segment(D, E)\nline_EB = scene.add.line_segment(E, B)\nline_BD = scene.add.line_segment(B, D)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.line_intersects_circle_at(line_BC, circle1, B, C)\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.perpendicular(line_BC, line_CD)\nscene.relate.point_lies_on(F, circle1)\nscene.relate.point_lies_on(G, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(line_BC.length, line_CD.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('C'), scene.get_object('D')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "square1": "square(B, C, D, E)", "semicircle1": "major_arc(F, G, H)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_DE": "line_segment(D, E)", "line_EB": "line_segment(E, B)", "line_BD": "line_segment(B, D)", "line_CF": "line_segment(C, F)"}, "Rels": ["line_intersects_circle_at(line_BC, circle1, B, C)", "is_diameter(line_BD, circle1)", "perpendicular(line_BC, line_CD)", "point_lies_on(F, circle1)", "point_lies_on(G, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_BC').length, scene.get_object('line_CD').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('C'), scene.get_object('D')), 90)"], "possible_solution": {"points": {"A": [0.7523805027762132, -0.4530087949653422], "B": [1.8398032492304557, 0.7565722959929443], "C": [1.9619611555391023, -1.5404323385525858], "D": [-0.3350430033273922, -1.6625902114948699], "E": [-0.45720088455234603, 0.6344147819044207], "F": [-0.8565077288547268, -0.2141457395757162], "G": [0.4975894740604179, 1.1534338555451136], "H": [-0.7930158392363815, 1.7093465749605599]}, "circles": {"A": 1.6265225075524004}}}
{"unique_id": "3obj_5rel_2extra_gen0077", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a rhomboid BCDE. There is a minor arc FG. There is a line segment BD. There is a line segment CF. There is a line segment AG. There is a line segment FE. Line BD intersects line CF at point H. Points B, H, and D are collinear. Line BD is a chord of the circle. Point F lies on the circle. Point G lies on the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ncircle1 = scene.add.circle(A)\nrhomboid1 = scene.add.rhomboid(B, C, D, E)\nminor_arc1 = scene.add.minor_arc(A, F, G)\nline_BD = scene.add.line_segment(B, D)\nline_CF = scene.add.line_segment(C, F)\nline_AG = scene.add.line_segment(A, G)\nline_FE = scene.add.line_segment(F, E)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_BD, line_CF, H)\nscene.relate.collinear(B, H, D)\nscene.relate.is_chord(line_BD, circle1)\nscene.relate.point_lies_on(F, circle1)\nscene.relate.point_lies_on(G, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "rhomboid1": "rhomboid(B, C, D, E)", "minor_arc1": "minor_arc(A, F, G)", "line_BD": "line_segment(B, D)", "line_CF": "line_segment(C, F)", "line_AG": "line_segment(A, G)", "line_FE": "line_segment(F, E)"}, "Rels": ["lines_intersect_at(line_BD, line_CF, H)", "collinear(B, H, D)", "is_chord(line_BD, circle1)", "point_lies_on(F, circle1)", "point_lies_on(G, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [0.33266155958971855, 2.5066500885193452], "B": [1.0596788278414162, -1.942869050014783], "C": [3.1801484723124243, 1.1935433845591041], "D": [0.25316433369430646, 7.014471590013902], "E": [-1.867305337702812, 3.878059239372173], "F": [-1.30539258259034, -1.6937728697854608], "G": [3.454348024984139, 5.759625358222712], "H": [0.9089137847474693, -0.2684369578001175]}, "circles": {"A": 4.508522421540046}}}
{"unique_id": "3obj_5rel_2extra_gen0083", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a trapezoid ABCD. There is a trapezoid EFGH. There is a circle with center I. There is a line segment AB. There is a line segment CD. There is a line segment EF. There is a line segment GH. There is a line segment IF. There is a line segment IH. There is a line segment AC. There is a line segment BD. Line IF is the perpendicular bisector of line AB. Trapezoids ABCD and EFGH are similar. Line IF is a radius of the circle. Line IH is a radius of the circle. Point F lies on the circle. Further, the lengths of line IF and line IH are equal, and the area of trapezoid ABCD is no greater than 20.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\ntrapezoid1 = scene.add.trapezoid(A, B, C, D)\ntrapezoid2 = scene.add.trapezoid(E, F, G, H)\ncircle1 = scene.add.circle(I)\nline_AB = scene.add.line_segment(A, B)\nline_CD = scene.add.line_segment(C, D)\nline_EF = scene.add.line_segment(E, F)\nline_GH = scene.add.line_segment(G, H)\nline_IF = scene.add.line_segment(I, F)\nline_IH = scene.add.line_segment(I, H)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\n\n### relationships\n\nscene.relate.perpendicular_bisector_at(line_AB, line_IF)\nscene.relate.similar(trapezoid1, trapezoid2)\nscene.relate.is_radius(line_IF, circle1)\nscene.relate.is_radius(line_IH, circle1)\nscene.relate.point_lies_on(F, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(line_IF.length, line_IH.length)\nscene.constraint.leq(trapezoid1.area, 20)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "trapezoid(A, B, C, D)", "trapezoid2": "trapezoid(E, F, G, H)", "circle1": "circle(I)", "line_AB": "line_segment(A, B)", "line_CD": "line_segment(C, D)", "line_EF": "line_segment(E, F)", "line_GH": "line_segment(G, H)", "line_IF": "line_segment(I, F)", "line_IH": "line_segment(I, H)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)"}, "Rels": ["perpendicular_bisector_at(line_AB, line_IF)", "similar(trapezoid1, trapezoid2)", "is_radius(line_IF, circle1)", "is_radius(line_IH, circle1)", "point_lies_on(F, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_IF').length, scene.get_object('line_IH').length)", "scene.constraint.leq(scene.get_object('trapezoid1').area, 20)"], "possible_solution": {"points": {"A": [1.0403855756229634, -0.8323515571815677], "B": [-1.7594503433884903, 3.6072847292359813], "C": [0.12996183982808265, -2.6360608889466244], "D": [-3.0227577108851666, 2.3631599667354157], "E": [-4.313538866417594, -2.036831526112785], "F": [1.5486006498148641, 2.350210048701971], "G": [-6.922926840384613, -0.9714460615145784], "H": [-0.32190980715731843, 3.968535959707844], "I": [-2.0504822166940135, 0.08040160964958389]}, "circles": {"I": 4.255060106337221}}}
{"unique_id": "3obj_5rel_2extra_gen0092", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J. There is a parallelogram with vertices A, B, C, D. There is a semicircle with center E and endpoints F and G. There is a semicircle with center H and endpoints I and J. There is a line segment AC. There is a line segment BD. Point F lies on the semicircle with center E. Point G lies on the semicircle with center E. Point I lies on the semicircle with center H. Point J lies on the semicircle with center H. The angle FEG is a right angle. Further, the radius of the semicircle with center E is equal to 3 units. Further, the perimeter of the parallelogram with vertices A, B, C, D is less than or equal to 20 units.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\"])\n\nparallelogram1 = scene.add.parallelogram(A, B, C, D)\nsemicircle1 = scene.add.major_arc(E, F, G)\nsemicircle2 = scene.add.major_arc(H, I, J)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\n\n### relationships\n\nscene.relate.point_lies_on(F, semicircle1)\nscene.relate.point_lies_on(G, semicircle1)\nscene.relate.point_lies_on(I, semicircle2)\nscene.relate.point_lies_on(J, semicircle2)\nscene.relate.right_angle(F, E, G)\n\n### Extra relationships\n\nscene.constraint.eq(semicircle1.radius, 3.0)\nscene.constraint.leq(parallelogram1.perimeter, 20.0)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"parallelogram1": "parallelogram(A, B, C, D)", "semicircle1": "MajorArc(E, F, G)", "semicircle2": "MajorArc(H, I, J)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)"}, "Rels": ["point_lies_on(F, semicircle1)", "point_lies_on(G, semicircle1)", "point_lies_on(I, semicircle2)", "point_lies_on(J, semicircle2)", "right_angle(F, E, G)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J"], "extra_rel": ["scene.constraint.eq(scene.get_object('semicircle1').radius, 3.0)", "scene.constraint.leq(scene.get_object('parallelogram1').perimeter, 20.0)"], "possible_solution": {"points": {"A": [0.5786584219037657, -0.44104089448634465], "B": [-3.359931822042104, 1.9847390652819719], "C": [-3.766467870601188, 0.7909883588730755], "D": [0.17212235859980207, -1.6347915894969098], "E": [1.6937345629471054, -1.319424221878075], "F": [-0.09334703802597832, 1.090210491387112], "G": [4.103369277188934, 0.4676573813862488], "H": [2.8118210169725977, 4.266753590315682], "I": [-3.1681102315300946, 2.46226249442342], "J": [4.3090418835040305, -1.7974112770387678]}, "circles": {}}}
{"unique_id": "3obj_5rel_2extra_gen0124", "nl_description": "Diagram description: The diagram contains points A, B, C, O, D, E, F. There is an obtuse triangle ABC. There is a circle with center O. There is an acute triangle DEF. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment OA. There is a line segment OB. There is a line segment OC. The circle is the circumcircle of triangle ABC. Line AD is a chord of the circle. Line BE is an altitude of triangle ABC from vertex B. Line CF is a median of triangle ABC from vertex C. Line OA is perpendicular to line BE.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"O\", \"D\", \"E\", \"F\"])\n\ntriangle1 = scene.add.obtuse_triangle(A, B, C)\ncircle1 = scene.add.circle(O)\ntriangle2 = scene.add.acute_triangle(D, E, F)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_OA = scene.add.line_segment(O, A)\nline_OB = scene.add.line_segment(O, B)\nline_OC = scene.add.line_segment(O, C)\n\n### relationships\n\nscene.relate.is_circumcircle(circle1, triangle1)\nscene.relate.is_chord(line_AD, circle1)\nscene.relate.is_altitude(line_BE, triangle1, B)\nscene.relate.is_median(line_CF, triangle1, C)\nscene.relate.perpendicular(line_OA, line_BE)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "obtuse_triangle(A, B, C)", "circle1": "circle(O)", "triangle2": "acute_triangle(D, E, F)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_OA": "line_segment(O, A)", "line_OB": "line_segment(O, B)", "line_OC": "line_segment(O, C)"}, "Rels": ["is_circumcircle(circle1, triangle1)", "is_chord(line_AD, circle1)", "is_altitude(line_BE, triangle1, B)", "is_median(line_CF, triangle1, C)", "perpendicular(line_OA, line_BE)"], "Points": ["A", "B", "C", "O", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [0.20958191940992324, 3.1625649528979913], "B": [0.08092864987553768, 2.4207053674883405], "C": [-1.4806738641105093, 2.6915189539606272], "O": [-0.6355454183432563, 2.9270425474884805], "D": [0.030178375492718273, 3.498464765995471], "E": [-0.10164358376214187, 3.075832334647084], "F": [0.14525502151517306, 2.7916343096591394]}, "circles": {"O": 0.8773318243089885}}}
{"unique_id": "3obj_5rel_2extra_gen0125", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a right triangle with vertices B, C, D. There is a trapezoid with vertices E, F, G, H. There is a line segment BC. There is a line segment CD. There is a line segment EF. There is a line segment FG. Point B lies on the circle. Point C lies on the circle. Line BC is a chord of the circle. Line BC is perpendicular to line CD. Line BC intersects line FG at point C. Further, the length of line BC is equal to the length of line CD and the angle at point C in triangle BCD is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ncircle1 = scene.add.circle(A)\nright_triangle1 = scene.add.right_triangle(B, C, D)\ntrapezoid1 = scene.add.trapezoid(E, F, G, H)\nline_BC = scene.add.line_segment(B, C)\nline_CD = scene.add.line_segment(C, D)\nline_EF = scene.add.line_segment(E, F)\nline_FG = scene.add.line_segment(F, G)\n\n### relationships\n\nscene.relate.point_lies_on(B, circle1)\nscene.relate.point_lies_on(C, circle1)\nscene.relate.is_chord(line_BC, circle1)\nscene.relate.perpendicular(line_BC, line_CD)\nscene.relate.lines_intersect_at(line_BC, line_FG, C)\n\n### Extra relationships\n\nscene.constraint.eq(line_BC.length, line_CD.length)\nscene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('C'), scene.get_object('D')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "right_triangle1": "right_triangle(B, C, D)", "trapezoid1": "trapezoid(E, F, G, H)", "line_BC": "line_segment(B, C)", "line_CD": "line_segment(C, D)", "line_EF": "line_segment(E, F)", "line_FG": "line_segment(F, G)"}, "Rels": ["point_lies_on(B, circle1)", "point_lies_on(C, circle1)", "is_chord(line_BC, circle1)", "perpendicular(line_BC, line_CD)", "lines_intersect_at(line_BC, line_FG, C)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_BC').length, scene.get_object('line_CD').length)", "scene.constraint.eq(scene.angle(scene.get_object('B'), scene.get_object('C'), scene.get_object('D')), 90)"], "possible_solution": {"points": {"A": [-0.2516531433430755, 2.1501841531938717], "B": [-2.357665081938244, 1.4146395864353907], "C": [1.5848528367290164, 3.4165008050751418], "D": [3.5867139994441475, -0.5260169789517944], "E": [-3.0171047544534964, -2.1761354345207544], "F": [-1.6389732486227386, -0.8529240005618308], "G": [2.2505894794885513, 4.298158974581793], "H": [-1.2878058687660032, 0.9007726334742614]}, "circles": {"A": 2.2307649092005866}}}
{"unique_id": "3obj_5rel_2extra_gen0127", "nl_description": "Diagram description: The diagram contains points A, B, C, O, D, E, F. There is a triangle ABC with vertices A, B, C. There is a circle with center O. There is a minor arc EF with center D. There is a line segment AD. There is a line segment BE. The circle is the circumcircle of triangle ABC. Line AD is tangent to the circle at point A. Point E is the midpoint of line AD. Line BE is an altitude of triangle ABC from vertex B. Point F lies on the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O, D, E, F = scene.add.points([\"A\", \"B\", \"C\", \"O\", \"D\", \"E\", \"F\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\ncircleO = scene.add.circle(O)\nminor_arc_DE = scene.add.minor_arc(D, E, F)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\n\n### relationships\n\nscene.relate.is_circumcircle(circleO, triangleABC)\nscene.relate.tangent_to_circle(line_AD, circleO, A)\nscene.relate.is_midpoint(E, line_AD)\nscene.relate.is_altitude(line_BE, triangleABC, B)\nscene.relate.point_lies_on(F, circleO)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "circleO": "circle(O)", "minor_arc_DE": "minor_arc(D, E, F)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)"}, "Rels": ["is_circumcircle(circleO, triangleABC)", "tangent_to_circle(line_AD, circleO, A)", "is_midpoint(E, line_AD)", "is_altitude(line_BE, triangleABC, B)", "point_lies_on(F, circleO)"], "Points": ["A", "B", "C", "O", "D", "E", "F"], "extra_rel": [], "possible_solution": {"points": {"A": [2.863730312430393, -1.297397250531816], "B": [-9.64250661873753, 4.808103905163886], "C": [2.7786310687374, -1.478375347410955], "O": [-3.477868223694746, 1.574077151325437], "D": [3.0317110961041775, -0.9264654033491779], "E": [2.948988336086921, -1.11265243591914], "F": [3.090693971763037, -0.7313936412632404]}, "circles": {"O": 6.96140877282666}}}
{"unique_id": "3obj_5rel_2extra_gen0132", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a circle with center A. There is a trapezoid BCDE. There is an isosceles trapezoid FGHI. There is a line segment BD. There is a line segment CE. There is a line segment FH. There is a line segment GI. Line BD intersects the circle at points B and D. Line CE is tangent to the circle at point C. Line BD is parallel to line FH. Line GI is a diameter of the circle. Line CE is perpendicular to line BD.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\ncircle1 = scene.add.circle(A)\ntrapezoid1 = scene.add.trapezoid(B, C, D, E)\nisosceles_trapezoid1 = scene.add.isosceles_trapezoid(F, G, H, I)\nline_BD = scene.add.line_segment(B, D)\nline_CE = scene.add.line_segment(C, E)\nline_FH = scene.add.line_segment(F, H)\nline_GI = scene.add.line_segment(G, I)\n\n### relationships\n\nscene.relate.line_intersects_circle_at(line_BD, circle1, B, D)\nscene.relate.tangent_to_circle(line_CE, circle1, C)\nscene.relate.parallel(line_BD, line_FH)\nscene.relate.is_diameter(line_GI, circle1)\nscene.relate.perpendicular(line_CE, line_BD)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "trapezoid1": "trapezoid(B, C, D, E)", "isosceles_trapezoid1": "isosceles_trapezoid(F, G, H, I)", "line_BD": "line_segment(B, D)", "line_CE": "line_segment(C, E)", "line_FH": "line_segment(F, H)", "line_GI": "line_segment(G, I)"}, "Rels": ["line_intersects_circle_at(line_BD, circle1, B, D)", "tangent_to_circle(line_CE, circle1, C)", "parallel(line_BD, line_FH)", "is_diameter(line_GI, circle1)", "perpendicular(line_CE, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": [], "possible_solution": {"points": {"A": [0.018220669777951334, 0.09380463502776636], "B": [0.5050175240938737, -0.5874553910546281], "C": [0.0722734514462834, 0.9293694227608043], "D": [0.5887273977879812, 0.7066783581391846], "E": [0.5337124918648086, 0.8995200000662542], "F": [1.3398878573315303, -1.6156864775382793], "G": [-0.7151721573317398, -0.3102051345263866], "H": [1.4479833468886816, 0.055445046393235976], "I": [0.7516145194238042, 0.4978158139327915]}, "circles": {"A": 0.8373107481408569}}}
{"unique_id": "3obj_5rel_2extra_gen0137", "nl_description": "Diagram description: The diagram contains points A, B, C, O, M, N, P. There is a triangle ABC. There is a circle with center O. There is an isosceles trapezoid MNOP. There is a line AB. There is a line AC. There is a line BC. There is a line MO. There is a line NO. The circle with center O is the circumcircle of triangle ABC. Point A lies on the circle with center O. Point C lies on the circle with center O. Point M is the midpoint of line AC. Point P is the midpoint of line BC. Further, the length of line BC is equal to the length of line AC and the inradius of triangle ABC is 2.0 units.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O, M, N, P = scene.add.points([\"A\", \"B\", \"C\", \"O\", \"M\", \"N\", \"P\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\ncircleO = scene.add.circle(O)\nisosceles_trapezoidMNOP = scene.add.isosceles_trapezoid(M, N, O, P)\nline_AC = scene.add.line_segment(A, C)\nline_BC = scene.add.line_segment(B, C)\nline_AB = scene.add.line_segment(A, B)\nline_MO = scene.add.line_segment(M, O)\nline_NO = scene.add.line_segment(N, O)\n\n### relationships\n\nscene.relate.is_circumcircle(circleO, triangleABC)\nscene.relate.point_lies_on(A, circleO)\nscene.relate.point_lies_on(C, circleO)\nscene.relate.is_midpoint(M, line_AC)\nscene.relate.is_midpoint(P, line_BC)\n\n### Extra relationships\n\nscene.constraint.eq(line_BC.length, line_AC.length)\nscene.constraint.eq(triangleABC.inradius, 2.0)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "Triangle(A, B, C)", "circleO": "Circle(O)", "isosceles_trapezoidMNOP": "IsoscelesTrapezoid(M, N, O, P)", "line_AC": "line_segment(A, C)", "line_BC": "line_segment(B, C)", "line_AB": "line_segment(A, B)", "line_MO": "line_segment(M, O)", "line_NO": "line_segment(N, O)"}, "Rels": ["is_circumcircle(circleO, triangleABC)", "point_lies_on(A, circleO)", "point_lies_on(C, circleO)", "is_midpoint(M, line_AC)", "is_midpoint(P, line_BC)"], "Points": ["A", "B", "C", "O", "M", "N", "P"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_BC').length, scene.get_object('line_AC').length)", "scene.constraint.eq(scene.get_object('triangleABC').inradius, 2.0)"], "possible_solution": {"points": {"A": [-0.578045630253256, -5.14122251114965], "B": [-6.6098913127265195, -0.3258823959595523], "C": [-0.1819475412164403, 1.5404458248362056], "O": [-2.7374317757059483, -1.660636903510517], "M": [-0.3800067851783978, -1.800387852938624], "N": [-1.4799219227573324, 1.9878302639732024], "P": [-3.3959266115862183, 0.6072809776920136]}, "circles": {"O": 4.096025602723743}}}
{"unique_id": "3obj_5rel_2extra_gen0153", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is an obtuse triangle with vertices A, B, C. There is an isosceles triangle with vertices D, E, F. There is an obtuse triangle with vertices G, H, I. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment GH. There is a line segment HI. There is a line segment IG. Triangle ABC is similar to triangle GHI. Points A, D, and G are collinear. Line AD is perpendicular to line BE. Line CF is an altitude from vertex C to the opposite side of triangle ABC. Point F is the orthocenter of triangle DEF. Further, length of line AD is equal to length of line BE and angle ABC is 120 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\ntriangle1 = scene.add.obtuse_triangle(A, B, C)\ntriangle2 = scene.add.isosceles_triangle(D, E, F)\ntriangle3 = scene.add.obtuse_triangle(G, H, I)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_GH = scene.add.line_segment(G, H)\nline_HI = scene.add.line_segment(H, I)\nline_IG = scene.add.line_segment(I, G)\n\n### relationships\n\nscene.relate.similar(triangle1, triangle3)\nscene.relate.collinear(A, D, G)\nscene.relate.perpendicular(line_AD, line_BE)\nscene.relate.is_altitude(line_CF, triangle1, C)\nscene.relate.is_orthocenter(F, triangle2)\n\n### Extra relationships\n\nscene.constraint.eq(line_AD.length, line_BE.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 120)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "obtuse_triangle(A, B, C)", "triangle2": "isosceles_triangle(D, E, F)", "triangle3": "obtuse_triangle(G, H, I)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_GH": "line_segment(G, H)", "line_HI": "line_segment(H, I)", "line_IG": "line_segment(I, G)"}, "Rels": ["similar(triangle1, triangle3)", "collinear(A, D, G)", "perpendicular(line_AD, line_BE)", "is_altitude(line_CF, triangle1, C)", "is_orthocenter(F, triangle2)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AD').length, scene.get_object('line_BE').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 120)"], "possible_solution": {"points": {"A": [-1.5586056658409493, 1.8375930158630598], "B": [-0.7563276267057001, 1.3094244951074636], "C": [-1.025826020123192, -3.2831417480116576], "D": [1.2378734728264702, -0.1416815590170441], "E": [-2.73540688590773, -1.4868456846608684], "F": [1.1648078246011349, 0.0444456865886024], "G": [3.290008320952127, -1.5941514354591575], "H": [2.7322628401271163, -1.9327500706763012], "I": [-0.007858412238072241, -0.4301694901410634]}, "circles": {}}}
{"unique_id": "3obj_5rel_2extra_gen0164", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a right isosceles triangle ABC with AB = BC and right angle at B. There is a square DEFG. There is a circle with center H. There is a line segment AC. There is a line segment BD. There is a line segment HF. Line HF is a radius of the circle. The circle is the circumcircle of square DEFG. Line AC is perpendicular to line BD. Line BD is an altitude from vertex B to triangle ABC. The circle is the incircle of triangle ABC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangleABC = scene.add.right_isosceles_triangle(A, B, C)\nsquareDEFG = scene.add.square(D, E, F, G)\ncircleH = scene.add.circle(H)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_HF = scene.add.line_segment(H, F)\n\n### relationships\n\nscene.relate.is_radius(line_HF, circleH)\nscene.relate.is_circumcircle(circleH, squareDEFG)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.is_altitude(line_BD, triangleABC, B)\nscene.relate.is_incircle(circleH, triangleABC)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "right_isosceles_triangle(A, B, C)", "squareDEFG": "square(D, E, F, G)", "circleH": "circle(H)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_HF": "line_segment(H, F)"}, "Rels": ["is_radius(line_HF, circleH)", "is_circumcircle(circleH, squareDEFG)", "perpendicular(line_AC, line_BD)", "is_altitude(line_BD, triangleABC, B)", "is_incircle(circleH, triangleABC)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.342362537960365, 0.5032109653668568], "B": [0.10715216569502556, -1.0974306328751529], "C": [-1.4934893277668846, -1.546944909175208], "D": [-0.9179258850612625, -0.5218673668916884], "E": [-0.2549200101926566, -0.3356735797554055], "F": [-0.06872584143307747, -0.9986792318014301], "G": [-0.7317313293197181, -1.1848727141525428], "H": [-0.4933262374216931, -0.7602725419823508]}, "circles": {"H": 0.48695407196508217}}}
{"unique_id": "3obj_5rel_2extra_gen0165", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a rectangle with points A, B, C, D. There is a circle with center E. There is an isosceles triangle with vertices F, G, H. There is a line segment AC. There is a line segment EG. There is a line segment FH. The circle is the circumcircle of the rectangle. Point G is the orthocenter of triangle FGH. Points A, E, and C are collinear. Line AC is a diameter of the circle. Line EG is perpendicular to line FH.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\ncircle1 = scene.add.circle(E)\ntriangle1 = scene.add.isosceles_triangle(F, G, H)\nline_AC = scene.add.line_segment(A, C)\nline_EG = scene.add.line_segment(E, G)\nline_FH = scene.add.line_segment(F, H)\n\n### relationships\n\nscene.relate.is_circumcircle(circle1, rectangle1)\nscene.relate.is_orthocenter(G, triangle1)\nscene.relate.collinear(A, E, C)\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.perpendicular(line_EG, line_FH)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "circle1": "circle(E)", "triangle1": "isosceles_triangle(F, G, H)", "line_AC": "line_segment(A, C)", "line_EG": "line_segment(E, G)", "line_FH": "line_segment(F, H)"}, "Rels": ["is_circumcircle(circle1, rectangle1)", "is_orthocenter(G, triangle1)", "collinear(A, E, C)", "is_diameter(line_AC, circle1)", "perpendicular(line_EG, line_FH)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [-1.127866605006706, 5.149521142646265], "B": [-1.1167893043956225, 4.611180981632707], "C": [-0.5279694907407806, 4.623296809444388], "D": [-0.5390469474077574, 5.161637138102936], "E": [-0.8279181097398209, 4.886409043230868], "F": [-1.698179229613979, 1.800563143759895], "G": [-0.5437664611498585, 3.928039950357953], "H": [1.5837103105413286, 2.7736270865049795]}, "circles": {"E": 0.39899508325244437}}}
{"unique_id": "3obj_5rel_2extra_gen0167", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a right triangle ABC with right angle at B. There is a rhombus DEFG. There is a circle with center H. There is a line segment AC. There is a line segment HD. There is a line segment HF. Line AC is tangent to the circle at A. Points A, H, and D are collinear. Line HD is a radius of the circle. Line HF is a radius of the circle. Line HD is perpendicular to line HF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntriangle1 = scene.add.right_triangle(A, B, C)\nrhombus1 = scene.add.rhombus(D, E, F, G)\ncircle1 = scene.add.circle(H)\nline_AC = scene.add.line_segment(A, C)\nline_HD = scene.add.line_segment(H, D)\nline_HF = scene.add.line_segment(H, F)\n\n### relationships\n\nscene.relate.tangent_to_circle(line_AC, circle1, A)\nscene.relate.collinear(A, H, D)\nscene.relate.is_radius(line_HD, circle1)\nscene.relate.is_radius(line_HF, circle1)\nscene.relate.perpendicular(line_HD, line_HF)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "right_triangle(A, B, C)", "rhombus1": "rhombus(D, E, F, G)", "circle1": "circle(H)", "line_AC": "line_segment(A, C)", "line_HD": "line_segment(H, D)", "line_HF": "line_segment(H, F)"}, "Rels": ["tangent_to_circle(line_AC, circle1, A)", "collinear(A, H, D)", "is_radius(line_HD, circle1)", "is_radius(line_HF, circle1)", "perpendicular(line_HD, line_HF)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [1.5776005338182233, -0.0253775388693414], "B": [1.651631012163668, 0.25761330704482277], "C": [-0.6119916490108915, 0.849775275958865], "D": [1.3875840300626983, -0.5007950876322497], "E": [2.0561153625011914, -1.6002719511962056], "F": [1.720301483571225, -0.35809138315640626], "G": [1.0517699873976638, 0.7413849086021349], "H": [1.4825917618641484, -0.2630851681163384]}, "circles": {"H": 0.2559913344354024}}}
{"unique_id": "3obj_5rel_2extra_gen0181", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, O, I, J, K. There is a regular octagon with vertices A, B, C, D, E, F, G, H. There is a circle with center O. There is a scalene triangle with vertices I, J, K. There is a line segment OI. There is a line segment OJ. There is a line segment OK. There is a line segment IJ. There is a line segment JK. There is a line segment KI. The circle is the circumcircle of the regular octagon. Line OI is a radius of the circle. Line OJ is a radius of the circle. Line OK is a radius of the circle. The extension of line IJ intersects the circle at I and J.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, O, I, J, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"O\", \"I\", \"J\", \"K\"])\n\nregular_octagon1 = scene.add.regular_octagon(A, B, C, D, E, F, G, H)\ncircle1 = scene.add.circle(O)\nscalene_triangle1 = scene.add.scalene_triangle(I, J, K)\nline_OI = scene.add.line_segment(O, I)\nline_OJ = scene.add.line_segment(O, J)\nline_OK = scene.add.line_segment(O, K)\nline_IJ = scene.add.line_segment(I, J)\nline_JK = scene.add.line_segment(J, K)\nline_KI = scene.add.line_segment(K, I)\n\n### relationships\n\nscene.relate.is_circumcircle(circle1, regular_octagon1)\nscene.relate.is_radius(line_OI, circle1)\nscene.relate.is_radius(line_OJ, circle1)\nscene.relate.is_radius(line_OK, circle1)\nscene.relate.line_extension_intersects_circle_at(line_IJ, circle1, I, J)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"regular_octagon1": "regular_octagon(A, B, C, D, E, F, G, H)", "circle1": "circle(O)", "scalene_triangle1": "scalene_triangle(I, J, K)", "line_OI": "line_segment(O, I)", "line_OJ": "line_segment(O, J)", "line_OK": "line_segment(O, K)", "line_IJ": "line_segment(I, J)", "line_JK": "line_segment(J, K)", "line_KI": "line_segment(K, I)"}, "Rels": ["is_circumcircle(circle1, regular_octagon1)", "is_radius(line_OI, circle1)", "is_radius(line_OJ, circle1)", "is_radius(line_OK, circle1)", "line_extension_intersects_circle_at(line_IJ, circle1, I, J)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "O", "I", "J", "K"], "extra_rel": [], "possible_solution": {"points": {"A": [2.07274334779051, 3.444813114827126], "B": [-0.06997510108657087, 3.5597553019180146], "C": [-1.6663822463974554, 2.1259009564798896], "D": [-1.7813244334883436, -0.01681749239719141], "E": [-0.34747008805021895, -1.613224637708076], "F": [1.7952483608268621, -1.728166824798964], "G": [3.3916555061377465, -0.2943124793608395], "H": [3.506597693228635, 1.8484059695162416], "O": [0.8626366005533733, 0.9157940666571424], "I": [2.816202781782846, -1.095144454547004], "J": [-1.88243348327492, 1.4857807453438614], "K": [2.9868134896895153, 2.745593831354497]}, "circles": {"O": 2.8036216919750623}}}
{"unique_id": "3obj_5rel_2extra_gen0190", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a trapezoid ABCD. There is a rhomboid EFGH. There is a circle with center I. There is a line segment AB. There is a line segment CD. There is a line segment EF. There is a line segment FG. There is a line segment IJ. Line AB is parallel to line CD. Line EF intersects the circle at points J and K. Angle ABC is a right angle. Line AB is perpendicular to line EF. Line IJ is a radius of the circle. Further, the area of trapezoid ABCD equals the area of rhomboid EFGH and angle ABC is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\"])\n\ntrapezoid1 = scene.add.trapezoid(A, B, C, D)\nrhomboid1 = scene.add.rhomboid(E, F, G, H)\ncircle1 = scene.add.circle(I)\nline_AB = scene.add.line_segment(A, B)\nline_CD = scene.add.line_segment(C, D)\nline_EF = scene.add.line_segment(E, F)\nline_FG = scene.add.line_segment(F, G)\nline_IJ = scene.add.line_segment(I, J)\n\n### relationships\n\nscene.relate.parallel(line_AB, line_CD)\nscene.relate.line_intersects_circle_at(line_EF, circle1, J, K)\nscene.relate.right_angle(A, B, C)\nscene.relate.perpendicular(line_AB, line_EF)\nscene.relate.is_radius(line_IJ, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(trapezoid1.area, rhomboid1.area)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "trapezoid(A, B, C, D)", "rhomboid1": "rhomboid(E, F, G, H)", "circle1": "circle(I)", "line_AB": "line_segment(A, B)", "line_CD": "line_segment(C, D)", "line_EF": "line_segment(E, F)", "line_FG": "line_segment(F, G)", "line_IJ": "line_segment(I, J)"}, "Rels": ["parallel(line_AB, line_CD)", "line_intersects_circle_at(line_EF, circle1, J, K)", "right_angle(A, B, C)", "perpendicular(line_AB, line_EF)", "is_radius(line_IJ, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K"], "extra_rel": ["scene.constraint.eq(scene.get_object('trapezoid1').area, scene.get_object('rhomboid1').area)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('B'), scene.get_object('C')), 90)"], "possible_solution": {"points": {"A": [-3.961047016857106, 0.013796195364947724], "B": [-0.342490295030027, -1.8253626002408814], "C": [1.2661039961299363, 1.3395568080083535], "D": [2.3342979704776132, 0.7966385119892695], "E": [0.22532952568105366, 2.501807891998321], "F": [-0.9556769365459628, 0.17816904363799524], "G": [-3.9474035876985556, -1.4080092007492426], "H": [-2.76639594570321, 0.9156329391375818], "I": [-0.018604894235861168, 0.09593550378906386], "J": [-0.7480460714268519, 0.5866848776406871], "K": [-0.8449799050895248, 0.3959720644706714]}, "circles": {"I": 0.879157113468181}}}
{"unique_id": "3obj_5rel_2extra_gen0198", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a circle with center A. There is a trapezoid BCDE. There is a square FGHI. There is a line segment BD. There is a line segment FH. There is a line segment CG. Line BD is the perpendicular bisector of line CG. Point G lies on the circle. Line FH is a diameter of the circle. The circle is the circumcircle of square FGHI. Line CG intersects the circle at points C and G.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\ncircle1 = scene.add.circle(A)\ntrapezoid1 = scene.add.trapezoid(B, C, D, E)\nsquare1 = scene.add.square(F, G, H, I)\nline_BD = scene.add.line_segment(B, D)\nline_FH = scene.add.line_segment(F, H)\nline_CG = scene.add.line_segment(C, G)\n\n### relationships\n\nscene.relate.perpendicular_bisector_at(line_BD, line_CG)\nscene.relate.point_lies_on(G, circle1)\nscene.relate.is_diameter(line_FH, circle1)\nscene.relate.is_circumcircle(circle1, square1)\nscene.relate.line_intersects_circle_at(line_CG, circle1, C, G)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "trapezoid1": "trapezoid(B, C, D, E)", "square1": "square(F, G, H, I)", "line_BD": "line_segment(B, D)", "line_FH": "line_segment(F, H)", "line_CG": "line_segment(C, G)"}, "Rels": ["perpendicular_bisector_at(line_BD, line_CG)", "point_lies_on(G, circle1)", "is_diameter(line_FH, circle1)", "is_circumcircle(circle1, square1)", "line_intersects_circle_at(line_CG, circle1, C, G)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": [], "possible_solution": {"points": {"A": [2.2456296554955224, -1.0941925007311022], "B": [2.061290427152939, -1.200026209763008], "C": [1.7804862799596588, -1.244099952820455], "D": [1.1825490418312623, -1.7045193994562466], "E": [3.095656125922938, -1.4042470907885307], "F": [2.57173862162933, -1.4581773357781866], "G": [1.8816446198231154, -1.420301281201957], "H": [1.9195210689229283, -0.7302072918745428], "I": [2.609614910677312, -0.7680833461846106]}, "circles": {"A": 0.4887040884128104}}}
{"unique_id": "3obj_5rel_2extra_gen0212", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a trapezoid ABCD. There is a circle with center E. There is a right triangle FGH. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment FH. Line AC is perpendicular to line BD. Point G is the orthocenter of triangle FGH. Line FH is a chord of the circle. Point F lies on the circle. Point H lies on the circle. Further, the length of line AC is equal to the length of line BD. Further, the area of triangle FGH is 6.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ntrapezoid1 = scene.add.trapezoid(A, B, C, D)\ncircle1 = scene.add.circle(E)\nright_triangle1 = scene.add.right_triangle(F, G, H)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\nline_FH = scene.add.line_segment(F, H)\n\n### relationships\n\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.is_orthocenter(G, right_triangle1)\nscene.relate.is_chord(line_FH, circle1)\nscene.relate.point_lies_on(F, circle1)\nscene.relate.point_lies_on(H, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.eq(right_triangle1.area, 6)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "trapezoid(A, B, C, D)", "circle1": "circle(E)", "right_triangle1": "right_triangle(F, G, H)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)", "line_FH": "line_segment(F, H)"}, "Rels": ["perpendicular(line_AC, line_BD)", "is_orthocenter(G, right_triangle1)", "is_chord(line_FH, circle1)", "point_lies_on(F, circle1)", "point_lies_on(H, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.eq(scene.get_object('right_triangle1').area, 6)"], "possible_solution": {"points": {"A": [1.9099804186342122, -0.9002787595614182], "B": [3.8682172383188784, -2.689868654119244], "C": [3.1725592080475358, -0.8434644616929051], "D": [3.8114029492434582, -1.4272898238796483], "E": [-1.148260656498374, -1.9834836895614192], "F": [-3.17806365976328, 0.32391754322288724], "G": [-1.597770712031996, -2.499509462435174], "H": [1.638537443153342, -0.6881238753652325]}, "circles": {"E": 3.073141821935172}}}
{"unique_id": "3obj_5rel_2extra_gen0219", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a triangle ABC. There is a circle with center D. There is a scalene triangle EFG. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment EG. There is a line segment FG. Line AD is a radius of the circle. Line BE is congruent to line CF. Line BE is an altitude of triangle ABC from vertex B. The circle is the circumcircle of triangle ABC. The circle is the incircle of triangle EFG.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntriangle1 = scene.add.triangle(A, B, C)\ncircle1 = scene.add.circle(D)\nscalene1 = scene.add.scalene_triangle(E, F, G)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_EG = scene.add.line_segment(E, G)\nline_FG = scene.add.line_segment(F, G)\n\n### relationships\n\nscene.relate.is_radius(line_AD, circle1)\nscene.relate.congruent(line_BE, line_CF)\nscene.relate.is_altitude(line_BE, triangle1, B)\nscene.relate.is_circumcircle(circle1, triangle1)\nscene.relate.is_incircle(circle1, scalene1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "Triangle(A, B, C)", "circle1": "Circle(D)", "scalene1": "ScaleneTriangle(E, F, G)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_EG": "line_segment(E, G)", "line_FG": "line_segment(F, G)"}, "Rels": ["is_radius(line_AD, circle1)", "congruent(line_BE, line_CF)", "is_altitude(line_BE, triangle1, B)", "is_circumcircle(circle1, triangle1)", "is_incircle(circle1, scalene1)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [-2.0316135795828094, 3.1872208623412206], "B": [-1.3213734331841396, 3.0945305638133225], "C": [-2.4286767128357507, 2.3290991518411293], "D": [-1.755124410340375, 2.538363088930617], "E": [-1.94169106263091, 3.3815590134058886], "F": [-3.081844605865782, 2.127730725619103], "G": [6.392268317931381, -0.11587166926936758]}, "circles": {"D": 0.7053103759778449}}}
{"unique_id": "3obj_5rel_2extra_gen0231", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E. There is a circle with center A. There is a circle with center B. There is a triangle with vertices C, D, E. There is a line segment CD. There is a line segment DE. There is a line segment EC. There is a line segment AD. circle with center A is the circumcircle of triangle CDE. circle with center B is the incircle of triangle CDE. angle DCE is a right angle. angle ECD is an obtuse angle. line AD is a radius of the circle with center A. Further, the diameter of the circle with center A is 4.0. Further, the area of triangle CDE is no greater than 6.0.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\"])\n\ncircle1 = scene.add.circle(A)\ncircle2 = scene.add.circle(B)\ntriangle1 = scene.add.triangle(C, D, E)\nline_CD = scene.add.line_segment(C, D)\nline_DE = scene.add.line_segment(D, E)\nline_EC = scene.add.line_segment(E, C)\nline_AD = scene.add.line_segment(A, D)\n\n### relationships\n\nscene.relate.is_circumcircle(circle1, triangle1)\nscene.relate.is_incircle(circle2, triangle1)\nscene.relate.right_angle(D, C, E)\nscene.relate.obtuse_angle(E, C, D)\nscene.relate.is_radius(line_AD, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(circle1.diameter, 4.0)\nscene.constraint.leq(triangle1.area, 6.0)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "circle2": "circle(B)", "triangle1": "triangle(C, D, E)", "line_CD": "line_segment(C, D)", "line_DE": "line_segment(D, E)", "line_EC": "line_segment(E, C)", "line_AD": "line_segment(A, D)"}, "Rels": ["is_circumcircle(circle1, triangle1)", "is_incircle(circle2, triangle1)", "right_angle(D, C, E)", "obtuse_angle(E, C, D)", "is_radius(line_AD, circle1)"], "Points": ["A", "B", "C", "D", "E"], "extra_rel": ["scene.constraint.eq(scene.get_object('circle1').diameter, 4.0)", "scene.constraint.leq(scene.get_object('triangle1').area, 6.0)"], "possible_solution": {"points": {"A": [-1.8278387033628931, 0.38561177819912623], "B": [-1.3538210649104947, -0.30330659114432384], "C": [-0.5867588792266588, -1.1827372423594427], "D": [-0.3851447770521254, 1.7707595389233153], "E": [-3.2704448220575104, -0.9996259222345417]}, "circles": {"A": 2.0000000715274475, "B": 0.8251741165329826}}}
{"unique_id": "3obj_5rel_2extra_gen0233", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L. There is a right trapezoid ABCD. There is a right trapezoid EFGH. There is a major arc IJK. There is a line segment AD. There is a line segment EH. There is a line segment IJ. There is a line segment JK. The angle ADB is acute. The extensions of line AD and line EH intersect at point L. Trapezoid ABCD and trapezoid EFGH are mirror images across line IJ. Line AD is perpendicular to line IJ. Point J lies on major arc IJK. Further, the area of trapezoid ABCD equals the area of trapezoid EFGH, and the angle ADB equals 60 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K, L = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"L\"])\n\ntrapezoid1 = scene.add.right_trapezoid(A, B, C, D)\ntrapezoid2 = scene.add.right_trapezoid(E, F, G, H)\nsemicircle1 = scene.add.major_arc(I, J, K)\nline_AD = scene.add.line_segment(A, D)\nline_EH = scene.add.line_segment(E, H)\nline_IJ = scene.add.line_segment(I, J)\nline_JK = scene.add.line_segment(J, K)\n\n### relationships\n\nscene.relate.acute_angle(A, D, B)\nscene.relate.line_extensions_intersect_at(line_AD, line_EH, L)\nscene.relate.mirror_across_line(trapezoid1, trapezoid2, line_IJ)\nscene.relate.perpendicular(line_AD, line_IJ)\nscene.relate.point_lies_on(J, semicircle1)\n\n### Extra relationships\n\nscene.constraint.eq(trapezoid1.area, trapezoid2.area)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('B')), 60)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "right_trapezoid(A, B, C, D)", "trapezoid2": "right_trapezoid(E, F, G, H)", "semicircle1": "major_arc(I, J, K)", "line_AD": "line_segment(A, D)", "line_EH": "line_segment(E, H)", "line_IJ": "line_segment(I, J)", "line_JK": "line_segment(J, K)"}, "Rels": ["acute_angle(A, D, B)", "line_extensions_intersect_at(line_AD, line_EH, L)", "mirror_across_line(trapezoid1, trapezoid2, line_IJ)", "perpendicular(line_AD, line_IJ)", "point_lies_on(J, semicircle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L"], "extra_rel": ["scene.constraint.eq(scene.get_object('trapezoid1').area, scene.get_object('trapezoid2').area)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('B')), 60)"], "possible_solution": {"points": {"A": [-0.48869552138204364, -0.05695316302425117], "B": [2.1346893878011453, 0.712826650679488], "C": [-1.4746768244725512, 1.2987500455575023], "D": [-0.9331300697442125, 1.4576511069407274], "E": [-1.0872879035881287, 1.9830142545527123], "F": [1.536082787599672, 2.7528065318197137], "G": [-1.1843615683145101, 0.30951152159683254], "H": [-0.6428552066767977, 0.46841211679518147], "I": [2.1029418095918393, 1.8113325969734655], "J": [0.047245227240164965, 1.2081191685084927], "K": [-0.01669128273127425, 1.5000329721122365], "L": [-0.41656124140994777, -0.3027827504949292]}, "circles": {}}}
{"unique_id": "3obj_5rel_2extra_gen0235", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a quadrilateral with vertices A, B, C, D. There is a rhombus with vertices E, F, G, H. There is an obtuse triangle with vertices I, J, K. There is a line segment AC. There is a line segment BD. There is a line segment EG. There is a line segment FH. The quadrilateral ABCD is similar to the rhombus EFGH. Point A lies on line segment AC. Point C lies on line segment AC. Line segment AC is perpendicular to line segment BD. Angle JKI is obtuse. Further, the length of line segment AC is equal to the length of line segment BD and the area of the obtuse triangle IJK is less than or equal to 10 square units.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\"])\n\nquadrilateral1 = scene.add.quadrilateral(A, B, C, D)\nrhombus1 = scene.add.rhombus(E, F, G, H)\nobtuse_triangle1 = scene.add.obtuse_triangle(I, J, K)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EG = scene.add.line_segment(E, G)\nline_FH = scene.add.line_segment(F, H)\n\n### relationships\n\nscene.relate.similar(quadrilateral1, rhombus1)\nscene.relate.point_lies_on(A, line_AC)\nscene.relate.point_lies_on(C, line_AC)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.obtuse_angle(J, K, I)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.leq(obtuse_triangle1.area, 10)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"quadrilateral1": "quadrilateral(A, B, C, D)", "rhombus1": "rhombus(E, F, G, H)", "obtuse_triangle1": "obtuse_triangle(I, J, K)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EG": "line_segment(E, G)", "line_FH": "line_segment(F, H)"}, "Rels": ["similar(quadrilateral1, rhombus1)", "point_lies_on(A, line_AC)", "point_lies_on(C, line_AC)", "perpendicular(line_AC, line_BD)", "obtuse_angle(J, K, I)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.leq(scene.get_object('obtuse_triangle1').area, 10)"], "possible_solution": {"points": {"A": [-2.458786128491576, 2.445631068020519], "B": [1.8611181306067965, 1.6306405448685555], "C": [1.0461484180989122, -2.6893640569494752], "D": [-3.2738820591899302, -1.874299227301349], "E": [0.16487932126732943, -0.9748981560579464], "F": [-0.20140920822571656, -0.3732828694477458], "G": [-0.8030405619904605, -0.739574174595832], "H": [-0.4367338766130182, -1.3412037296411372], "I": [-0.006666392941107213, -2.9398449622027947], "J": [3.2633694245250773, 3.4696986267726535], "K": [0.5185097749071861, -3.058957699463344]}, "circles": {}}}
{"unique_id": "3obj_5rel_2extra_gen0244", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a circle with center A. There is a regular pentagon with vertices B, C, D, E, F. There is a square with vertices G, H, I, J. There is a line segment BD. There is a line segment GI. Line BD and line GI intersect at point K. Points B, K, D are collinear. Line BD is perpendicular to line GI. The circle is the circumcircle of the regular pentagon. The circle is the incircle of the square.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\"])\n\ncircle1 = scene.add.circle(A)\npentagon1 = scene.add.regular_pentagon(B, C, D, E, F)\nsquare1 = scene.add.square(G, H, I, J)\nline_BD = scene.add.line_segment(B, D)\nline_GI = scene.add.line_segment(G, I)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_BD, line_GI, K)\nscene.relate.collinear(B, K, D)\nscene.relate.perpendicular(line_BD, line_GI)\nscene.relate.is_circumcircle(circle1, pentagon1)\nscene.relate.is_incircle(circle1, square1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "pentagon1": "regular_pentagon(B, C, D, E, F)", "square1": "square(G, H, I, J)", "line_BD": "line_segment(B, D)", "line_GI": "line_segment(G, I)"}, "Rels": ["lines_intersect_at(line_BD, line_GI, K)", "collinear(B, K, D)", "perpendicular(line_BD, line_GI)", "is_circumcircle(circle1, pentagon1)", "is_incircle(circle1, square1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K"], "extra_rel": [], "possible_solution": {"points": {"A": [0.49690271094904737, 1.7236339226453756], "B": [0.37355770308289965, 2.362315863571758], "C": [-0.14863752572746228, 1.803690112765573], "D": [0.22127993466311632, 1.134428087132664], "E": [0.9720967270268988, 1.2794271587181074], "F": [1.0662095636413103, 2.0383035389279995], "G": [1.4098353442152525, 1.610414886597755], "H": [0.38368390854919887, 0.8106997630202877], "I": [-0.4160314843475873, 1.836851500927711], "J": [0.6101197878626722, 2.6365666074490837], "K": [0.2974184617267572, 1.748372841931512]}, "circles": {"A": 0.6504849894254094}}}
{"unique_id": "3obj_5rel_2extra_gen0246", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a regular pentagon with vertices A, B, C, D, E. There is a rectangle with vertices F, G, H, I. There is a circle with center J. There are line segments AC, FG, JH, JI. The extensions of line AC and line FG intersect at point K. Angle AKF is acute. The circle is the circumcircle of the regular pentagon. The line segment JH is a radius of the circle. Line JI is perpendicular to line FG. Further, the diagonal of the regular pentagon is equal to two times the radius of the circle, and the length of line JI is less than or equal to one-eighth of the perimeter of the rectangle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\"])\n\npentagon1 = scene.add.regular_pentagon(A, B, C, D, E)\nrectangle1 = scene.add.rectangle(F, G, H, I)\ncircle1 = scene.add.circle(J)\nline_AC = scene.add.line_segment(A, C)\nline_FG = scene.add.line_segment(F, G)\nline_JH = scene.add.line_segment(J, H)\nline_JI = scene.add.line_segment(J, I)\n\n### relationships\n\nscene.relate.line_extensions_intersect_at(line_AC, line_FG, K)\nscene.relate.acute_angle(A, K, F)\nscene.relate.is_circumcircle(circle1, pentagon1)\nscene.relate.is_radius(line_JH, circle1)\nscene.relate.perpendicular(line_JI, line_FG)\n\n### Extra relationships\n\nscene.constraint.eq(pentagon1.diagonal, 2 * circle1.radius)\nscene.constraint.leq(line_JI.length, rectangle1.perimeter / 8)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"pentagon1": "regular_pentagon(A, B, C, D, E)", "rectangle1": "rectangle(F, G, H, I)", "circle1": "circle(J)", "line_AC": "line_segment(A, C)", "line_FG": "line_segment(F, G)", "line_JH": "line_segment(J, H)", "line_JI": "line_segment(J, I)"}, "Rels": ["line_extensions_intersect_at(line_AC, line_FG, K)", "acute_angle(A, K, F)", "is_circumcircle(circle1, pentagon1)", "is_radius(line_JH, circle1)", "perpendicular(line_JI, line_FG)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K"], "extra_rel": ["scene.constraint.eq(scene.get_object('pentagon1').diagonal, 2 * scene.get_object('circle1').radius)", "scene.constraint.leq(scene.get_object('line_JI').length, scene.get_object('rectangle1').perimeter / 8)"], "possible_solution": {"points": {"A": [0.6929876771614039, 2.5094047837529367], "B": [0.8532702946622779, 2.1164020809634247], "C": [1.2765681287825204, 2.147395394789229], "D": [1.377897960132171, 2.5595530189470797], "E": [1.0172254058603074, 2.7832871255732323], "F": [0.7237468398251513, 3.042576346446478], "G": [0.9825354822526332, 3.174419478475944], "H": [1.2093151788513612, 2.7279403038825305], "I": [0.9501719709261323, 2.5967441815281167], "J": [1.0436279202780854, 2.422692414291634], "K": [0.23490380055349444, 2.7935688270337042]}, "circles": {"J": 0.3469431646543426}}}
{"unique_id": "3obj_5rel_2extra_gen0255", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a major arc with center A from B to C. There is a circle with center D. There is a major arc with center E from F to G. There is a line segment AD. There is a line segment BD. There is a line segment EG. Line AD is a radius of the circle. Line EG is a chord of the circle. Line AD and line BD intersect at D. Line AD is perpendicular to line BD. Point F lies on the major arc with center E from F to G.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\nsemicircle1 = scene.add.major_arc(A, B, C)\ncircle1 = scene.add.circle(D)\nsemicircle2 = scene.add.major_arc(E, F, G)\nline_AD = scene.add.line_segment(A, D)\nline_BD = scene.add.line_segment(B, D)\nline_EG = scene.add.line_segment(E, G)\n\n### relationships\n\nscene.relate.is_radius(line_AD, circle1)\nscene.relate.lines_intersect_at(line_AD, line_BD, D)\nscene.relate.is_chord(line_EG, circle1)\nscene.relate.perpendicular(line_AD, line_BD)\nscene.relate.point_lies_on(F, semicircle2)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"semicircle1": "major_arc(A, B, C)", "circle1": "circle(D)", "semicircle2": "major_arc(E, F, G)", "line_AD": "line_segment(A, D)", "line_BD": "line_segment(B, D)", "line_EG": "line_segment(E, G)"}, "Rels": ["is_radius(line_AD, circle1)", "lines_intersect_at(line_AD, line_BD, D)", "is_chord(line_EG, circle1)", "perpendicular(line_AD, line_BD)", "point_lies_on(F, semicircle2)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [0.3601468368235071, 0.7379360373248641], "B": [-0.03888261180068012, -1.368213251646415], "C": [-1.0355000624100354, -0.8891039274523614], "D": [-0.23482636026643783, 0.6810465872457767], "E": [-0.008022093675385684, 0.12806432306664636], "F": [-0.43852197313181807, 0.15845122729546135], "G": [0.30521193002882474, 0.4249446905031558]}, "circles": {"D": 0.5976867876661139}}}
{"unique_id": "3obj_5rel_2extra_gen0266", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a kite with vertices A, B, C, D. There is a regular pentagon with vertices E, F, G, H, I. There is a circle with center J. There is a line segment AC. There is a line segment BD. There is a line segment EG. There is a line segment JE. Line AC is the perpendicular bisector of line BD. The extensions of lines AC and EG intersect at point K. Line BD is the angle bisector of angle ABD. The circle with center J is the circumcircle of the regular pentagon. Line JE is a radius of the circle with center J.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\"])\n\nkite1 = scene.add.kite(A, B, C, D)\npentagon1 = scene.add.regular_pentagon(E, F, G, H, I)\ncircle1 = scene.add.circle(J)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EG = scene.add.line_segment(E, G)\nline_JE = scene.add.line_segment(J, E)\n\n### relationships\n\nscene.relate.perpendicular_bisector_at(line_AC, line_BD)\nscene.relate.line_extensions_intersect_at(line_AC, line_EG, K)\nscene.relate.angle_bisector(A, B, D, line_BD)\nscene.relate.is_circumcircle(circle1, pentagon1)\nscene.relate.is_radius(line_JE, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"kite1": "kite(A, B, C, D)", "pentagon1": "regular_pentagon(E, F, G, H, I)", "circle1": "circle(J)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EG": "line_segment(E, G)", "line_JE": "line_segment(J, E)"}, "Rels": ["perpendicular_bisector_at(line_AC, line_BD)", "line_extensions_intersect_at(line_AC, line_EG, K)", "angle_bisector(A, B, D, line_BD)", "is_circumcircle(circle1, pentagon1)", "is_radius(line_JE, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K"], "extra_rel": [], "possible_solution": {"points": {"A": [-3.6473449456607656, 0.7941101259247458], "B": [-9.79689697305299, -4.533849597034459], "C": [-3.7776590126154694, 0.9445173542064319], "D": [2.50057705374066, 6.120663645325033], "E": [3.716125606617898, 1.250113873265486], "F": [0.6554148049440955, 2.912373991336556], "G": [-1.8713001647091214, 0.5151316644653902], "H": [-0.37218509416416606, -2.628705690881946], "I": [3.08103394213303, -2.174461704717015], "J": [1.0417950399253395, -0.02505798531817792], "K": [-3.2481506581894863, 0.33401513083136014]}, "circles": {"J": 2.9627887756412608}}}
{"unique_id": "3obj_5rel_2extra_gen0275", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K, L, O, P, Q. There is a rectangle with vertices A, B, C, D. There is a quadrilateral with vertices E, F, G, H. There is a quadrilateral with vertices I, J, K, L. There is a line segment AC. There is a line segment BD. There is a line segment EG. There is a line segment FH. There is a line segment IK. There is a line segment JL. Line AC intersects line BD at O. Line EG intersects line FH at P. Line IK intersects line JL at Q. The angle between OA and OB at O is acute. The angle between EP and FP at P is a right angle. Further, the perimeter of the rectangle equals the perimeter of the quadrilateral with vertices E, F, G, H. Further, the length of line AC is less than or equal to the length of line EG.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K, L, O, P, Q = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"L\", \"O\", \"P\", \"Q\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\nquad1 = scene.add.quadrilateral(E, F, G, H)\nquad2 = scene.add.quadrilateral(I, J, K, L)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EG = scene.add.line_segment(E, G)\nline_FH = scene.add.line_segment(F, H)\nline_IK = scene.add.line_segment(I, K)\nline_JL = scene.add.line_segment(J, L)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_BD, O)\nscene.relate.lines_intersect_at(line_EG, line_FH, P)\nscene.relate.lines_intersect_at(line_IK, line_JL, Q)\nscene.relate.acute_angle(A, O, B)\nscene.relate.right_angle(E, P, F)\n\n### Extra relationships\n\nscene.constraint.eq(rectangle1.perimeter, quad1.perimeter)\nscene.constraint.leq(line_AC.length, line_EG.length)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "quad1": "quadrilateral(E, F, G, H)", "quad2": "quadrilateral(I, J, K, L)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EG": "line_segment(E, G)", "line_FH": "line_segment(F, H)", "line_IK": "line_segment(I, K)", "line_JL": "line_segment(J, L)"}, "Rels": ["lines_intersect_at(line_AC, line_BD, O)", "lines_intersect_at(line_EG, line_FH, P)", "lines_intersect_at(line_IK, line_JL, Q)", "acute_angle(A, O, B)", "right_angle(E, P, F)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "O", "P", "Q"], "extra_rel": ["scene.constraint.eq(scene.get_object('rectangle1').perimeter, scene.get_object('quad1').perimeter)", "scene.constraint.leq(scene.get_object('line_AC').length, scene.get_object('line_EG').length)"], "possible_solution": {"points": {"A": [-2.418695334434267, 2.9334166230168974], "B": [-1.769485205779758, 2.5101079710542535], "C": [-3.2964270508098146, 0.1683033427791953], "D": [-3.945636957307428, 0.591611953406339], "E": [0.43813845091397724, 3.4890421704144052], "F": [0.148553773619724, 3.3864646215638206], "G": [-0.9770061338108342, 0.4347940159452277], "H": [0.7501733794564913, 3.1077021077539313], "I": [-1.8797939777572572, -2.694095545291679], "J": [-2.12157893770665, 0.020507076724341638], "K": [1.1335530171367556, 4.974742499124845], "L": [0.9918255207747103, 0.7269314660717404], "O": [-2.8575613604316197, 1.5508602825796696], "P": [0.3478277664237599, 3.294128340915321], "Q": [-0.6850601212721853, 0.34645027594126265]}, "circles": {}}}
{"unique_id": "3obj_5rel_2extra_gen0299", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a major arc with center A, start point B, and end point C. There is a circle with center D. There is an isosceles trapezoid with vertices E, F, G, H. There is a line segment AD. There is a line segment BD. There is a line segment EF. There is a line segment GH. Point A lies on the circle. Point B lies on the circle. Line AD is a radius of the circle. Line BD is a radius of the circle. Point E lies on the major arc. Further, length of line EF is equal to length of line AD and angle ADB is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\nsemicircle1 = scene.add.major_arc(A, B, C)\ncircle1 = scene.add.circle(D)\ntrapezoid1 = scene.add.isosceles_trapezoid(E, F, G, H)\nline_AD = scene.add.line_segment(A, D)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\nline_GH = scene.add.line_segment(G, H)\n\n### relationships\n\nscene.relate.point_lies_on(A, circle1)\nscene.relate.point_lies_on(B, circle1)\nscene.relate.is_radius(line_AD, circle1)\nscene.relate.is_radius(line_BD, circle1)\nscene.relate.point_lies_on(E, semicircle1)\n\n### Extra relationships\n\nscene.constraint.eq(line_EF.length, line_AD.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('B')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"semicircle1": "major_arc(A, B, C)", "circle1": "circle(D)", "trapezoid1": "isosceles_trapezoid(E, F, G, H)", "line_AD": "line_segment(A, D)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)", "line_GH": "line_segment(G, H)"}, "Rels": ["point_lies_on(A, circle1)", "point_lies_on(B, circle1)", "is_radius(line_AD, circle1)", "is_radius(line_BD, circle1)", "point_lies_on(E, semicircle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_EF').length, scene.get_object('line_AD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('D'), scene.get_object('B')), 90)"], "possible_solution": {"points": {"A": [-5.488973645289408, -2.666541983314698], "B": [1.150385524764633, -2.7748881006088193], "C": [-2.417889515195442, -8.553924336861586], "D": [-2.2234671377634183, -6.040394630000926], "E": [0.7515248278301019, -4.935684642510924], "F": [-2.5478243355182086, -8.276449499042903], "G": [-2.6139841629969185, -2.1519576365074324], "H": [0.6853651455988768, 1.1888073706456663]}, "circles": {"D": 4.695360968110288}}}
{"unique_id": "3obj_5rel_2extra_gen0302", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a rhomboid ABCD. There is a minor arc EFG. There is a circle with center H. There is a line segment AC. There is a line segment BD. There is a line segment FG. Line AC and line BD intersect at I. Angle AIB is a right angle. Line FG is a chord of the circle. Point F lies on the circle. Point G lies on the circle. Further, length of line AC equals length of line BD. Further, area of the minor arc EFG equals half the area of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\nrhomboid1 = scene.add.rhomboid(A, B, C, D)\narc1 = scene.add.minor_arc(E, F, G)\ncircle1 = scene.add.circle(H)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_FG = scene.add.line_segment(F, G)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_BD, I)\nscene.relate.right_angle(A, I, B)\nscene.relate.is_chord(line_FG, circle1)\nscene.relate.point_lies_on(F, circle1)\nscene.relate.point_lies_on(G, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.eq(arc1.area, (1/2) * circle1.area)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rhomboid1": "rhomboid(A, B, C, D)", "arc1": "minor_arc(E, F, G)", "circle1": "circle(H)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_FG": "line_segment(F, G)"}, "Rels": ["lines_intersect_at(line_AC, line_BD, I)", "right_angle(A, I, B)", "is_chord(line_FG, circle1)", "point_lies_on(F, circle1)", "point_lies_on(G, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.eq(scene.get_object('arc1').area, (1/2) * scene.get_object('circle1').area)"], "possible_solution": {"points": {"A": [0.17116275797606256, -1.2756500607755696], "B": [0.13683149739697023, -1.6080372101619527], "C": [0.4697894674630505, -1.6423776678841715], "D": [0.5039945866238438, -1.3099616647079333], "E": [2.0622916518543244, -0.5100522626089112], "F": [-2.1609578096663564, 0.3959742300223614], "G": [2.938643562187043, 3.7194558456283113], "H": [0.4730529647363805, 1.9285034693195666], "I": [0.32028278586258263, -1.4589441918169492]}, "circles": {"H": 3.0474018342110827}}}
{"unique_id": "3obj_5rel_2extra_gen0306", "nl_description": "Diagram description: The diagram contains points A, B, C, O, H, Q, M, N, P. There is a triangle ABC. There is a quadrilateral MNOP. There is a circle with center O. There are line segments AH and BC. The circle is the circumcircle of triangle ABC. H is the orthocenter of triangle ABC. Line AH and line BC intersect at H. Q is the midpoint of line BC. Q lies on line BC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, O, H, Q, M, N, P = scene.add.points([\"A\", \"B\", \"C\", \"O\", \"H\", \"Q\", \"M\", \"N\", \"P\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\ncircleO = scene.add.circle(O)\nquadrilateralMNOP = scene.add.quadrilateral(M, N, O, P)\nlineAH = scene.add.line_segment(A, H)\nlineBC = scene.add.line_segment(B, C)\n\n### relationships\n\nscene.relate.is_circumcircle(circleO, triangleABC)\nscene.relate.is_orthocenter(H, triangleABC)\nscene.relate.lines_intersect_at(lineAH, lineBC, H)\nscene.relate.is_midpoint(Q, lineBC)\nscene.relate.point_lies_on(Q, lineBC)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "circleO": "circle(O)", "quadrilateralMNOP": "quadrilateral(M, N, O, P)", "lineAH": "line_segment(A, H)", "lineBC": "line_segment(B, C)"}, "Rels": ["is_circumcircle(circleO, triangleABC)", "is_orthocenter(H, triangleABC)", "lines_intersect_at(lineAH, lineBC, H)", "is_midpoint(Q, lineBC)", "point_lies_on(Q, lineBC)"], "Points": ["A", "B", "C", "O", "H", "Q", "M", "N", "P"], "extra_rel": [], "possible_solution": {"points": {"A": [7.783295011327334, -9.39601783266162], "B": [-2.0167546153162395, 3.63189172253189], "C": [-1.374405735522864, 4.102927988821102], "O": [3.1220823484465847, -2.702438520704737], "H": [-1.8536696869311597, 3.7459544499874524], "Q": [-1.6954875131417892, 3.867464565708462], "M": [0.5827690726127768, -7.908428113716563], "N": [-8.46144503577401, 8.664808126648488], "P": [9.882142707738105, -4.028799265988982]}, "circles": {"O": 8.15667792451266}}}
{"unique_id": "3obj_5rel_2extra_gen0311", "nl_description": "Diagram description: The diagram contains points A, B, C, D, O. There is a triangle ABC. There is a kite ABCD. There is a circle with center O. There is a line segment AD. There is a line segment BC. There is a line segment AC. There is a line segment OA. There is a line segment OC. Point A lies on the circle. Point C lies on the circle. Line OA is a radius of the circle. Line OC is a radius of the circle. Line AD is congruent to line AC.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, O = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"O\"])\n\ntriangleABC = scene.add.triangle(A, B, C)\nkiteABCD = scene.add.kite(A, B, C, D)\ncircleO = scene.add.circle(O)\nline_AD = scene.add.line_segment(A, D)\nline_BC = scene.add.line_segment(B, C)\nline_AC = scene.add.line_segment(A, C)\nline_OA = scene.add.line_segment(O, A)\nline_OC = scene.add.line_segment(O, C)\n\n### relationships\n\nscene.relate.point_lies_on(A, circleO)\nscene.relate.point_lies_on(C, circleO)\nscene.relate.is_radius(line_OA, circleO)\nscene.relate.is_radius(line_OC, circleO)\nscene.relate.congruent(line_AD, line_AC)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangleABC": "triangle(A, B, C)", "kiteABCD": "kite(A, B, C, D)", "circleO": "circle(O)", "line_AD": "line_segment(A, D)", "line_BC": "line_segment(B, C)", "line_AC": "line_segment(A, C)", "line_OA": "line_segment(O, A)", "line_OC": "line_segment(O, C)"}, "Rels": ["point_lies_on(A, circleO)", "point_lies_on(C, circleO)", "is_radius(line_OA, circleO)", "is_radius(line_OC, circleO)", "congruent(line_AD, line_AC)"], "Points": ["A", "B", "C", "D", "O"], "extra_rel": [], "possible_solution": {"points": {"A": [-0.5758437712082531, 0.36255390258617876], "B": [4.655073602230966, 0.010845456802080931], "C": [0.3386851602599154, -2.9648873973550938], "D": [2.763069499107737, -0.509161361244873], "O": [0.9143516377995295, -1.017271375687051]}, "circles": {"O": 2.03091115009402}}}
{"unique_id": "3obj_5rel_2extra_gen0319", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I, J, K. There is a square with vertices A, B, C, D. There is a parallelogram with vertices E, F, G, H. There is a right triangle with vertices I, J, K. There is a line segment AC. There is a line segment EG. There is a line segment IJ. Square ABCD is similar to the parallelogram EFGH. Points A, C, and E are collinear. Line AC is perpendicular to line EG. Line IJ is an altitude of the right triangle IJK from vertex I. Point J is the orthocenter of the right triangle IJK.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I, J, K = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\"])\n\nsquare1 = scene.add.square(A, B, C, D)\nparallelogram1 = scene.add.parallelogram(E, F, G, H)\nright_triangle1 = scene.add.right_triangle(I, J, K)\nline_AC = scene.add.line_segment(A, C)\nline_EG = scene.add.line_segment(E, G)\nline_IJ = scene.add.line_segment(I, J)\n\n### relationships\n\nscene.relate.similar(square1, parallelogram1)\nscene.relate.collinear(A, C, E)\nscene.relate.perpendicular(line_AC, line_EG)\nscene.relate.is_altitude(line_IJ, right_triangle1, I)\nscene.relate.is_orthocenter(J, right_triangle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"square1": "square(A, B, C, D)", "parallelogram1": "parallelogram(E, F, G, H)", "right_triangle1": "right_triangle(I, J, K)", "line_AC": "line_segment(A, C)", "line_EG": "line_segment(E, G)", "line_IJ": "line_segment(I, J)"}, "Rels": ["similar(square1, parallelogram1)", "collinear(A, C, E)", "perpendicular(line_AC, line_EG)", "is_altitude(line_IJ, right_triangle1, I)", "is_orthocenter(J, right_triangle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K"], "extra_rel": [], "possible_solution": {"points": {"A": [-3.3786892933628363, -4.98102331883059], "B": [-3.3517573112336443, -3.77595705774139], "C": [-2.1464379494818115, -3.803005657984982], "D": [-2.173363872740142, -5.0080669559260595], "E": [1.6617904892964193, -0.1623420090422925], "F": [1.6755965900759207, 0.4379705575919513], "G": [1.0750824967622592, 0.45172598119265006], "H": [1.0612734511103556, -0.14858390157534687], "I": [-7.929494578385999, -2.1273638590254094], "J": [2.430952674243669, -2.9830007958739855], "K": [3.018147482387997, 4.127047960699654]}, "circles": {}}}
{"unique_id": "3obj_5rel_2extra_gen0328", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a minor arc BC. There is a parallelogram DEFG. There is a line segment BE. There is a line segment CF. There is a line segment DE. There is a line segment AF. Points B, A, and C are collinear. Line BE is a chord of the circle. Line CF intersects line BE at point H. Line AF is a radius of the circle. Line DE is perpendicular to line AF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ncircle1 = scene.add.circle(A)\nminor_arc1 = scene.add.minor_arc(A, B, C)\nparallelogram1 = scene.add.parallelogram(D, E, F, G)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_DE = scene.add.line_segment(D, E)\nline_AF = scene.add.line_segment(A, F)\n\n### relationships\n\nscene.relate.collinear(B, A, C)\nscene.relate.lines_intersect_at(line_BE, line_CF, H)\nscene.relate.is_chord(line_BE, circle1)\nscene.relate.is_radius(line_AF, circle1)\nscene.relate.perpendicular(line_DE, line_AF)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "minor_arc1": "minor_arc(A, B, C)", "parallelogram1": "parallelogram(D, E, F, G)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_DE": "line_segment(D, E)", "line_AF": "line_segment(A, F)"}, "Rels": ["collinear(B, A, C)", "lines_intersect_at(line_BE, line_CF, H)", "is_chord(line_BE, circle1)", "is_radius(line_AF, circle1)", "perpendicular(line_DE, line_AF)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [0.2619977321048704, 1.4782572651313044], "B": [-3.243031302057931, 1.591143870994004], "C": [3.7670268174936647, 1.365370796688381], "D": [0.8103059655477497, -2.3530089491294226], "E": [0.08166446132621126, -2.0239494016387503], "F": [-1.181358514976368, -1.7177863206784527], "G": [-0.4527151831427859, -2.0468459266026806], "H": [-0.5574262206336391, -1.3290368736054035]}, "circles": {"A": 3.506846367387619}}}
{"unique_id": "3obj_5rel_2extra_gen0330", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a trapezoid ABCD. There is a circle with center E. There is an isosceles trapezoid FGHI. There is a line segment AC. There is a line segment BD. There is a line segment EF. Line AC intersects the circle at points A and C. Trapezoid ABCD is similar to isosceles trapezoid FGHI. Line AC is perpendicular to line BD. Line EF is a radius of the circle. Point F lies on the circle. Further, the area of trapezoid ABCD is equal to the area of isosceles trapezoid FGHI, and angle AEF is 90 degrees.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\ntrapezoid1 = scene.add.trapezoid(A, B, C, D)\ncircle1 = scene.add.circle(E)\nisosceles_trapezoid1 = scene.add.isosceles_trapezoid(F, G, H, I)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\n\n### relationships\n\nscene.relate.line_intersects_circle_at(line_AC, circle1, A, C)\nscene.relate.similar(trapezoid1, isosceles_trapezoid1)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.is_radius(line_EF, circle1)\nscene.relate.point_lies_on(F, circle1)\n\n### Extra relationships\n\nscene.constraint.eq(trapezoid1.area, isosceles_trapezoid1.area)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('E'), scene.get_object('F')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "trapezoid(A, B, C, D)", "circle1": "circle(E)", "isosceles_trapezoid1": "isosceles_trapezoid(F, G, H, I)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)"}, "Rels": ["line_intersects_circle_at(line_AC, circle1, A, C)", "similar(trapezoid1, isosceles_trapezoid1)", "perpendicular(line_AC, line_BD)", "is_radius(line_EF, circle1)", "point_lies_on(F, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": ["scene.constraint.eq(scene.get_object('trapezoid1').area, scene.get_object('isosceles_trapezoid1').area)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('E'), scene.get_object('F')), 90)"], "possible_solution": {"points": {"A": [0.6533501855845887, -2.2288220667255936], "B": [1.0405380315290667, 0.544729829428236], "C": [0.48017499716469975, -1.999120621588919], "D": [0.8110763447331524, 0.37143717127214143], "E": [-0.2097854156484109, -2.698829449938366], "F": [0.2602230580525976, -3.56196658132014], "G": [0.6036040461817807, -0.785439263720645], "H": [0.08364745987813586, -3.3352282659077392], "I": [0.3771071527000161, -0.9621279074665966]}, "circles": {"E": 0.9827973932943166}}}
{"unique_id": "3obj_5rel_2extra_gen0331", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is an acute triangle with vertices B, C, D. There is a rhombus with vertices E, F, G, H. There is a line segment BD. There is a line segment CF. Line BD is an altitude of the acute triangle from vertex B. The circle is the circumcircle of the acute triangle. Line BD is perpendicular to line CF. Point F lies on the circle. Point G is the midpoint of line CF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ncircle1 = scene.add.circle(A)\nacute_tri1 = scene.add.acute_triangle(B, C, D)\nrhombus1 = scene.add.rhombus(E, F, G, H)\nline_BD = scene.add.line_segment(B, D)\nline_CF = scene.add.line_segment(C, F)\n\n### relationships\n\nscene.relate.is_altitude(line_BD, acute_tri1, B)\nscene.relate.is_circumcircle(circle1, acute_tri1)\nscene.relate.perpendicular(line_BD, line_CF)\nscene.relate.point_lies_on(F, circle1)\nscene.relate.is_midpoint(G, line_CF)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "acute_tri1": "acute_triangle(B, C, D)", "rhombus1": "rhombus(E, F, G, H)", "line_BD": "line_segment(B, D)", "line_CF": "line_segment(C, F)"}, "Rels": ["is_altitude(line_BD, acute_tri1, B)", "is_circumcircle(circle1, acute_tri1)", "perpendicular(line_BD, line_CF)", "point_lies_on(F, circle1)", "is_midpoint(G, line_CF)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [0.4061842883368953, -0.26747579267814336], "B": [-6.905938556632015, 1.908191371619348], "C": [7.65872362393806, -2.6328181304869354], "D": [-6.9606390991294065, 1.7150946538597895], "E": [-1.8150082580437283, -4.057305577629144], "F": [-7.009689074993928, 1.5212728601588734], "G": [0.3245864661370235, -0.5556844700275455], "H": [5.519268157590716, -6.134271009618543]}, "circles": {"A": 7.628551066039161}}}
{"unique_id": "3obj_5rel_2extra_gen0333", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G. There is a triangle with points A, B, C. There is a circle with center G. There is a line segment AD. There is a line segment BE. There is a line segment CF. There is a line segment GE. There is a line segment AG. Line AD is a median of triangle ABC from vertex A. Line BE is a median of triangle ABC from vertex B. Point G is the centroid of triangle ABC. The circle with center G is the circumcircle of triangle ABC. Line AG is the angle bisector of angle GAF.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\"])\n\ntriangle1 = scene.add.triangle(A, B, C)\ncircle1 = scene.add.circle(G)\nline_AD = scene.add.line_segment(A, D)\nline_BE = scene.add.line_segment(B, E)\nline_CF = scene.add.line_segment(C, F)\nline_GE = scene.add.line_segment(G, E)\nline_AG = scene.add.line_segment(A, G)\n\n### relationships\n\nscene.relate.is_median(line_AD, triangle1, A)\nscene.relate.is_median(line_BE, triangle1, B)\nscene.relate.is_centroid(G, triangle1)\nscene.relate.is_circumcircle(circle1, triangle1)\nscene.relate.angle_bisector(G, A, F, line_AG)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"triangle1": "triangle(A, B, C)", "circle1": "circle(G)", "line_AD": "line_segment(A, D)", "line_BE": "line_segment(B, E)", "line_CF": "line_segment(C, F)", "line_GE": "line_segment(G, E)", "line_AG": "line_segment(A, G)"}, "Rels": ["is_median(line_AD, triangle1, A)", "is_median(line_BE, triangle1, B)", "is_centroid(G, triangle1)", "is_circumcircle(circle1, triangle1)", "angle_bisector(G, A, F, line_AG)"], "Points": ["A", "B", "C", "D", "E", "F", "G"], "extra_rel": [], "possible_solution": {"points": {"A": [5.492441224852184, 7.139389461194196], "B": [7.472393788324038, -5.60214242961386], "C": [-4.552072011943624, -0.9460416925269833], "D": [1.4601710008037587, -3.274101480995465], "E": [0.4701898815020566, 3.096672717837745], "F": [-0.4457232662896866, -8.196128898418385], "G": [2.8042591111832724, 0.197066717596141]}, "circles": {"G": 7.444608014997439}}}
{"unique_id": "3obj_5rel_2extra_gen0351", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a rectangle with vertices A, B, C, D. There is an equilateral triangle with vertices E, F, G. There is a circle with center H. There is a line segment AC. There is a line segment EF. There is a line segment HD. Line AC is a diameter of the circle. H is the centroid of the triangle with vertices E, F, G. Line AC is perpendicular to line EF. Point D lies on the circle. Line HD is a radius of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\nrectangle1 = scene.add.rectangle(A, B, C, D)\ntriangle1 = scene.add.equilateral_triangle(E, F, G)\ncircle1 = scene.add.circle(H)\nline_AC = scene.add.line_segment(A, C)\nline_EF = scene.add.line_segment(E, F)\nline_HD = scene.add.line_segment(H, D)\n\n### relationships\n\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.is_centroid(H, triangle1)\nscene.relate.perpendicular(line_AC, line_EF)\nscene.relate.point_lies_on(D, circle1)\nscene.relate.is_radius(line_HD, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rectangle1": "rectangle(A, B, C, D)", "triangle1": "equilateral_triangle(E, F, G)", "circle1": "circle(H)", "line_AC": "line_segment(A, C)", "line_EF": "line_segment(E, F)", "line_HD": "line_segment(H, D)"}, "Rels": ["is_diameter(line_AC, circle1)", "is_centroid(H, triangle1)", "perpendicular(line_AC, line_EF)", "point_lies_on(D, circle1)", "is_radius(line_HD, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [0.14357321713476015, 0.7929608484318226], "B": [0.05326543196400506, 0.5298588920479735], "C": [0.4058859331322581, 0.4088250856367234], "D": [0.49619303343786986, 0.6719259456129671], "E": [0.5016309054121387, 1.0729460990461266], "F": [-0.2475301374703128, 0.5613701387584918], "G": [0.5700883552970042, 0.16836526732280474], "H": [0.2747297644401717, 0.6008937564943049]}, "circles": {"H": 0.2325762557383485}}}
{"unique_id": "3obj_5rel_2extra_gen0354", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is an isosceles trapezoid ABCD. There is an equilateral triangle EFG. There is a circle with center H. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment HG. Line AC intersects line BD at point I. Point I is the centroid of trapezoid ABCD. The circle is the circumcircle of triangle EFG. Line HG is a radius of the circle. Line AC is perpendicular to line BD. Further, the length of line AC is equal to the length of line BD. Further, angle AIB is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\ntrapezoid1 = scene.add.isosceles_trapezoid(A, B, C, D)\ntriangle1 = scene.add.equilateral_triangle(E, F, G)\ncircle1 = scene.add.circle(H)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\nline_HG = scene.add.line_segment(H, G)\n\n### relationships\n\nscene.relate.lines_intersect_at(line_AC, line_BD, I)\nscene.relate.is_centroid(I, trapezoid1)\nscene.relate.is_circumcircle(circle1, triangle1)\nscene.relate.is_radius(line_HG, circle1)\nscene.relate.perpendicular(line_AC, line_BD)\n\n### Extra relationships\n\nscene.constraint.eq(line_AC.length, line_BD.length)\nscene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('I'), scene.get_object('B')), 90)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"trapezoid1": "isosceles_trapezoid(A, B, C, D)", "triangle1": "equilateral_triangle(E, F, G)", "circle1": "circle(H)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)", "line_HG": "line_segment(H, G)"}, "Rels": ["lines_intersect_at(line_AC, line_BD, I)", "is_centroid(I, trapezoid1)", "is_circumcircle(circle1, triangle1)", "is_radius(line_HG, circle1)", "perpendicular(line_AC, line_BD)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": ["scene.constraint.eq(scene.get_object('line_AC').length, scene.get_object('line_BD').length)", "scene.constraint.eq(scene.angle(scene.get_object('A'), scene.get_object('I'), scene.get_object('B')), 90)"], "possible_solution": {"points": {"A": [-2.490769666734819, -4.330998020215337], "B": [-4.873370536311192, -2.027840573565048], "C": [-2.5702230259593226, 0.3547722448130067], "D": [-0.18761842704068804, -1.9483871847133298], "E": [-0.6998908597616187, 0.7301703589964903], "F": [-5.580219021539587, -2.06343980343018], "G": [-5.559408910923119, 3.559857209254196], "H": [-3.946506062202726, 0.7422018238364191], "I": [-2.5304954594838787, -1.9881148919056528]}, "circles": {"H": 3.2466340982613535}}}
{"unique_id": "3obj_5rel_2extra_gen0355", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a circle with center A. There is a major arc BC on the circle. There is a trapezoid DEFG. There is a line segment DE. There is a line segment GF. There is a line segment DF. There is a line segment EG. Point B lies on the circle. Point C lies on the circle. The extensions of line DE and line GF intersect at point H. Line DF is a chord of the circle. Line EG is a diameter of the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\ncircle1 = scene.add.circle(A)\nmajor_arc1 = scene.add.major_arc(A, B, C)\ntrapezoid1 = scene.add.trapezoid(D, E, F, G)\nline_DE = scene.add.line_segment(D, E)\nline_GF = scene.add.line_segment(G, F)\nline_DF = scene.add.line_segment(D, F)\nline_EG = scene.add.line_segment(E, G)\n\n### relationships\n\nscene.relate.point_lies_on(B, circle1)\nscene.relate.point_lies_on(C, circle1)\nscene.relate.line_extensions_intersect_at(line_DE, line_GF, H)\nscene.relate.is_chord(line_DF, circle1)\nscene.relate.is_diameter(line_EG, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "major_arc1": "major_arc(A, B, C)", "trapezoid1": "trapezoid(D, E, F, G)", "line_DE": "line_segment(D, E)", "line_GF": "line_segment(G, F)", "line_DF": "line_segment(D, F)", "line_EG": "line_segment(E, G)"}, "Rels": ["point_lies_on(B, circle1)", "point_lies_on(C, circle1)", "line_extensions_intersect_at(line_DE, line_GF, H)", "is_chord(line_DF, circle1)", "is_diameter(line_EG, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [-3.3262589377744827, -2.8805771415877865], "B": [-3.1341879736687894, -2.7727036150100504], "C": [-3.533172530441807, -2.956180420927438], "D": [-3.3016124335222456, -2.662151968904442], "E": [-3.497417525434415, -2.7420914876307423], "F": [-3.3393644152418354, -3.100041828242193], "G": [-3.155089302129097, -3.0185734735713337], "H": [9.137807362855659, 2.416259278856422]}, "circles": {"A": 0.22009013712916226}}}
{"unique_id": "3obj_5rel_2extra_gen0360", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H. There is a rhombus with vertices A, B, C, D. There is a circle with center E. There is a minor arc with center E, starting at F and ending at G. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment EG. Line AC is the perpendicular bisector of line BD. Line AC and line BD intersect at point H. Line EF is a radius of the circle. Line EG is a radius of the circle. Point F lies on the circle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"])\n\nrhombus1 = scene.add.rhombus(A, B, C, D)\ncircle1 = scene.add.circle(E)\nminor_arc1 = scene.add.minor_arc(E, F, G)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\nline_EG = scene.add.line_segment(E, G)\n\n### relationships\n\nscene.relate.perpendicular_bisector_at(line_AC, line_BD)\nscene.relate.lines_intersect_at(line_AC, line_BD, H)\nscene.relate.is_radius(line_EF, circle1)\nscene.relate.is_radius(line_EG, circle1)\nscene.relate.point_lies_on(F, circle1)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"rhombus1": "rhombus(A, B, C, D)", "circle1": "circle(E)", "minor_arc1": "minor_arc(E, F, G)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)", "line_EG": "line_segment(E, G)"}, "Rels": ["perpendicular_bisector_at(line_AC, line_BD)", "lines_intersect_at(line_AC, line_BD, H)", "is_radius(line_EF, circle1)", "is_radius(line_EG, circle1)", "point_lies_on(F, circle1)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H"], "extra_rel": [], "possible_solution": {"points": {"A": [-1.7371481151473183, -0.8660986046504363], "B": [-0.09667682302804484, 1.3337529051499164], "C": [2.1197187963223967, -0.28429621439748076], "D": [0.47924754540764947, -2.484147699197343], "E": [0.16571415959024993, 0.5102983646011231], "F": [1.7267516586028842, 0.8348838037885942], "G": [0.6026330404886384, 2.0436918559469865], "H": [0.19128541664396784, -0.5751973840272495]}, "circles": {"E": 1.5944258165439618}}}
{"unique_id": "3obj_5rel_2extra_gen0370", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a quadrilateral ABCD. There is a rhombus EFGH. There is a circle with center I. There is a line segment AC. There is a line segment BD. There is a line segment EF. There is a line segment IH. Point A lies on the circle. Point C lies on the circle. Line AC is a diameter of the circle. Line AC is perpendicular to line BD. Angle BAD is a right angle.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\nquadrilateral1 = scene.add.quadrilateral(A, B, C, D)\nrhombus1 = scene.add.rhombus(E, F, G, H)\ncircle1 = scene.add.circle(I)\nline_AC = scene.add.line_segment(A, C)\nline_BD = scene.add.line_segment(B, D)\nline_EF = scene.add.line_segment(E, F)\nline_IH = scene.add.line_segment(I, H)\n\n### relationships\n\nscene.relate.point_lies_on(A, circle1)\nscene.relate.point_lies_on(C, circle1)\nscene.relate.is_diameter(line_AC, circle1)\nscene.relate.perpendicular(line_AC, line_BD)\nscene.relate.right_angle(B, A, D)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"quadrilateral1": "quadrilateral(A, B, C, D)", "rhombus1": "rhombus(E, F, G, H)", "circle1": "circle(I)", "line_AC": "line_segment(A, C)", "line_BD": "line_segment(B, D)", "line_EF": "line_segment(E, F)", "line_IH": "line_segment(I, H)"}, "Rels": ["point_lies_on(A, circle1)", "point_lies_on(C, circle1)", "is_diameter(line_AC, circle1)", "perpendicular(line_AC, line_BD)", "right_angle(B, A, D)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": [], "possible_solution": {"points": {"A": [1.4844147259397946, 0.586658905127067], "B": [-0.27364737396937394, 2.4143099883476022], "C": [0.9772454611030906, -1.4924402499684701], "D": [2.6444108833186912, 1.702487486269461], "E": [3.072527727181822, 1.428176775322521], "F": [1.3129754908549993, 0.0416653824729236], "G": [1.2507560079652225, 2.2809881484066716], "H": [3.0103081964369887, 3.6674995514829023], "I": [1.2308301285037102, -0.4528906411396432]}, "circles": {"I": 1.0700319592915806}}}
{"unique_id": "3obj_5rel_2extra_gen0395", "nl_description": "Diagram description: The diagram contains points A, B, C, D, E, F, G, H, I. There is a circle with center A. There is a rectangle B C D E. There is a kite F G H I. There is a line segment BD. There is a line segment FH. There is a line segment AC. Point B lies on the circle with center A. Point D lies on the circle with center A. Line BD is a diameter of the circle with center A. Line AC is a radius of the circle with center A. Line BD is perpendicular to line FH.", "pygeox_code": "from pygeox import GeoScene\n\nscene = GeoScene()\n\n### objects\n\nA, B, C, D, E, F, G, H, I = scene.add.points([\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\"])\n\ncircle1 = scene.add.circle(A)\nrectangle1 = scene.add.rectangle(B, C, D, E)\nkite1 = scene.add.kite(F, G, H, I)\nline_BD = scene.add.line_segment(B, D)\nline_FH = scene.add.line_segment(F, H)\nline_AC = scene.add.line_segment(A, C)\n\n### relationships\n\nscene.relate.point_lies_on(B, circle1)\nscene.relate.point_lies_on(D, circle1)\nscene.relate.is_diameter(line_BD, circle1)\nscene.relate.is_radius(line_AC, circle1)\nscene.relate.perpendicular(line_BD, line_FH)\n\nscene.solver.numerical()\nscene.plot()", "Objs": {"circle1": "circle(A)", "rectangle1": "rectangle(B, C, D, E)", "kite1": "kite(F, G, H, I)", "line_BD": "line_segment(B, D)", "line_FH": "line_segment(F, H)", "line_AC": "line_segment(A, C)"}, "Rels": ["point_lies_on(B, circle1)", "point_lies_on(D, circle1)", "is_diameter(line_BD, circle1)", "is_radius(line_AC, circle1)", "perpendicular(line_BD, line_FH)"], "Points": ["A", "B", "C", "D", "E", "F", "G", "H", "I"], "extra_rel": [], "possible_solution": {"points": {"A": [0.2023665663349494, 2.885352032623427], "B": [0.48076083952912235, 2.978556474581363], "C": [0.42051649702634636, 2.6888802724653313], "D": [-0.07602809556640262, 2.7921472278309034], "E": [-0.015783358560598662, 3.0818244508777806], "F": [-2.203658463859762, -1.0262961787543217], "G": [8.11975229967981, 2.323197740387603], "H": [-2.139442753585962, -1.2181052386842053], "I": [7.55915485364349, 2.13554275514015]}, "circles": {"A": 0.2935823099096503}}}