id int32 1 6.98k | annotation stringclasses 132
values | source stringlengths 7 17 | problem_level int32 0 28 | problem_text_cn stringlengths 20 201 | problem_text_en stringlengths 58 424 | problem_img stringlengths 5 8 | construction_cdl listlengths 1 28 | text_cdl listlengths 0 16 | image_cdl listlengths 0 16 | goal_cdl stringlengths 8 131 | problem_answer stringclasses 906
values | theorem_seqs listlengths 0 28 | theorem_seqs_dag_json stringlengths 13 3.3k | image imagewidth (px) 48 1.6k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
401 | NaZhu_2023-03-12 | Geometry3k-409 | 16 | 如图所示，PS=3，RY=5，WX=10，WY=8，XY=6，RP∥XW，RQ⊥PQ，WY垂直于XY，YS⊥PS。求直线PQ的长度。 | As shown in the diagram, PS=3, RY=5, WX=10, WY=8, XY=6, RP∥XW, RQ⊥PQ, WY⊥XY, YS⊥PS. Find the length of line PQ. | 401.png | [
"Shape(YR,RA,AY)",
"Shape(PY,YS,SP)",
"Shape(YA,AQ,QS,SY)",
"Shape(AX,XQ,QA)",
"Shape(SQ,QW,WS)",
"Collinear(YAX)",
"Collinear(YSW)",
"Collinear(PSQ)",
"Collinear(RAQ)",
"Collinear(RYP)",
"Collinear(XQW)"
] | [
"Equal(LengthOfLine(PS),3)",
"Equal(LengthOfLine(RY),5)",
"Equal(LengthOfLine(WX),10)",
"Equal(LengthOfLine(WY),8)",
"Equal(LengthOfLine(XY),6)",
"ParallelBetweenLine(RP,XW)",
"PerpendicularBetweenLine(RQ,PQ)",
"PerpendicularBetweenLine(WY,XY)",
"PerpendicularBetweenLine(YS,PS)"
] | [
"PerpendicularBetweenLine(RQ,PQ)",
"PerpendicularBetweenLine(WY,XY)",
"PerpendicularBetweenLine(YS,PS)"
] | Value(LengthOfLine(PQ)) | 6 | [
"parallel_property_collinear_extend(3,RP,XW,Y)",
"parallel_property_collinear_extend(3,WX,PY,Q)",
"adjacent_complementary_angle(1,QSY,YSP)",
"adjacent_complementary_angle(1,RAY,YAQ)",
"parallel_judgment_ipsilateral_internal_angle(1,QA,SY)",
"parallel_judgment_ipsilateral_internal_angle(1,SQ,YA)",
"paral... | {"START": ["parallel_property_collinear_extend(3,RP,XW,Y)", "adjacent_complementary_angle(1,QSY,YSP)", "adjacent_complementary_angle(1,RAY,YAQ)", "line_addition(1,PS,SQ)"], "adjacent_complementary_angle(1,QSY,YSP)": ["parallel_judgment_ipsilateral_internal_angle(1,QA,SY)", "parallel_judgment_ipsilateral_internal_angle(... | |
402 | JiaZou_2023-04-09 | Geometry3k-410 | 2 | 如图所示，YW=18，ZY=18，弧OYW的角度为143，⌒OZY的角度为2*x-1。求x的值。 | As shown in the diagram, YW=18, ZY=18, the measure of arc OYW is 143, the measure of arc OZY is 2*x-1. Find the value of x. | 402.png | [
"Shape(WY,OYW)",
"Shape(ZY,YW,OWZ)",
"Shape(YZ,OZY)",
"Cocircular(O,YWZ)"
] | [
"Equal(LengthOfLine(YW),18)",
"Equal(LengthOfLine(ZY),18)",
"Equal(MeasureOfArc(OYW),143)",
"Equal(MeasureOfArc(OZY),2*x-1)"
] | [
"Equal(LengthOfLine(YW),18)",
"Equal(LengthOfLine(ZY),18)",
"Equal(MeasureOfArc(OYW),143)",
"Equal(MeasureOfArc(OZY),2*x-1)"
] | Value(x) | 72 | [
"congruent_arc_judgment_chord_equal(1,OYW,OZY)",
"congruent_arc_property_measure_equal(1,OYW,OZY)"
] | {"START": ["congruent_arc_judgment_chord_equal(1,OYW,OZY)"], "congruent_arc_judgment_chord_equal(1,OYW,OZY)": ["congruent_arc_property_measure_equal(1,OYW,OZY)"]} | |
403 | NaZhu_2023-03-12 | Geometry3k-411 | 1 | 如图所示，AC=12，BA=13，BC=15。求∠ACB的大小。 | As shown in the diagram, AC=12, BA=13, BC=15. Find the measure of ∠ACB. | 403.png | [
"Shape(BA,AC,CB)"
] | [
"Equal(LengthOfLine(AC),12)",
"Equal(LengthOfLine(BA),13)",
"Equal(LengthOfLine(BC),15)"
] | [
"Equal(LengthOfLine(AC),12)",
"Equal(LengthOfLine(BA),13)",
"Equal(LengthOfLine(BC),15)"
] | Value(MeasureOfAngle(ACB)) | 180*acos(5/9)/pi | [
"cosine_theorem(1,CBA)"
] | {"START": ["cosine_theorem(1,CBA)"]} | |
404 | JiaZou_2023-04-09 | Geometry3k-412 | 2 | 如图所示，∠JQR=131°，QR∥TS，TQ平行于SR。求∠STC的大小。 | As shown in the diagram, ∠JQR=131°, QR is parallel to TS, TQ∥SR. Find the measure of ∠STC. | 404.png | [
"Shape(JQ,QR)",
"Shape(QR,RH)",
"Shape(QT,TS,SR,RQ)",
"Shape(ST,TC)",
"Shape(BS,ST)",
"Collinear(JQTC)",
"Collinear(HRSB)"
] | [
"Equal(MeasureOfAngle(JQR),131)",
"ParallelBetweenLine(QR,TS)",
"ParallelBetweenLine(TQ,SR)"
] | [
"Equal(MeasureOfAngle(JQR),131)",
"ParallelBetweenLine(QR,TS)",
"ParallelBetweenLine(TQ,SR)"
] | Value(MeasureOfAngle(STC)) | 49 | [
"parallel_property_corresponding_angle(1,QR,TS,J)",
"adjacent_complementary_angle(1,QTS,STC)"
] | {"START": ["parallel_property_corresponding_angle(1,QR,TS,J)", "adjacent_complementary_angle(1,QTS,STC)"]} | |
405 | JiaZou_2023-04-09 | Geometry3k-413 | 2 | 如图所示，∠ACB=125°，∠BCD=x°，∠DCA=121°。求x的值。 | As shown in the diagram, ∠ACB=125°, ∠BCD=x°, ∠DCA=121°. Find the value of x. | 405.png | [
"Shape(BC,CD,CDB)",
"Shape(AC,CB,CBA)",
"Shape(DC,CA,CAD)",
"Cocircular(C,ADB)"
] | [
"Equal(MeasureOfAngle(ACB),125)",
"Equal(MeasureOfAngle(BCD),x)",
"Equal(MeasureOfAngle(DCA),121)"
] | [
"Equal(MeasureOfAngle(ACB),125)",
"Equal(MeasureOfAngle(BCD),x)",
"Equal(MeasureOfAngle(DCA),121)"
] | Value(x) | 114 | [
"angle_addition(1,DCA,ACB)",
"round_angle(1,DCB,BCD)"
] | {"START": ["angle_addition(1,DCA,ACB)", "round_angle(1,DCB,BCD)"]} | |
406 | JiaZou_2023-04-09 | Geometry3k-414 | 5 | 如图所示，CA=10，CD=2，CE=t-2，EB=t+1，AB∥DE。求t的值。 | As shown in the diagram, CA=10, CD=2, CE=t-2, EB=t+1, AB is parallel to DE. Find the value of t. | 406.png | [
"Shape(AD,DE,EB,BA)",
"Shape(DC,CE,ED)",
"Collinear(ADC)",
"Collinear(CEB)"
] | [
"Equal(LengthOfLine(CA),10)",
"Equal(LengthOfLine(CD),2)",
"Equal(LengthOfLine(CE),t-2)",
"Equal(LengthOfLine(EB),t+1)",
"ParallelBetweenLine(AB,DE)"
] | [
"Equal(LengthOfLine(CA),10)",
"Equal(LengthOfLine(CD),2)",
"Equal(LengthOfLine(CE),t-2)",
"Equal(LengthOfLine(EB),t+1)",
"ParallelBetweenLine(AB,DE)"
] | Value(t) | 3 | [
"line_addition(1,CE,EB)",
"parallel_property_corresponding_angle(2,AB,DE,C)",
"similar_triangle_judgment_aa(1,EDC,BAC)",
"similar_triangle_property_line_ratio(1,EDC,BAC)",
"similar_triangle_property_line_ratio(1,DCE,ACB)"
] | {"START": ["line_addition(1,CE,EB)", "parallel_property_corresponding_angle(2,AB,DE,C)"], "parallel_property_corresponding_angle(2,AB,DE,C)": ["similar_triangle_judgment_aa(1,EDC,BAC)"], "similar_triangle_judgment_aa(1,EDC,BAC)": ["similar_triangle_property_line_ratio(1,EDC,BAC)", "similar_triangle_property_line_ratio(... | |
407 | NaZhu_2023-03-12 | Geometry3k-415 | 3 | 如图所示，AC=CB，AD=DC，∠ADC=92°。求∠DCA的大小。 | As shown in the diagram, AC=CB, AD=DC, ∠ADC=92°. Find the measure of ∠DCA. | 407.png | [
"Shape(AD,DC,CA)",
"Shape(AC,CB,BA)",
"Collinear(DCB)"
] | [
"Equal(LengthOfLine(AC),LengthOfLine(CB))",
"Equal(LengthOfLine(AD),LengthOfLine(DC))",
"Equal(MeasureOfAngle(ADC),92)"
] | [
"Equal(LengthOfLine(AC),LengthOfLine(CB))",
"Equal(LengthOfLine(AD),LengthOfLine(DC))",
"Equal(MeasureOfAngle(ADC),92)"
] | Value(MeasureOfAngle(DCA)) | 44 | [
"isosceles_triangle_judgment_line_equal(1,DCA)",
"isosceles_triangle_property_angle_equal(1,DCA)",
"triangle_property_angle_sum(1,ADC)"
] | {"START": ["isosceles_triangle_judgment_line_equal(1,DCA)", "triangle_property_angle_sum(1,ADC)"], "isosceles_triangle_judgment_line_equal(1,DCA)": ["isosceles_triangle_property_angle_equal(1,DCA)"]} | |
408 | JiaZou_2023-04-09 | Geometry3k-416 | 9 | 如图所示，弧DQS的角度为238，⊙D的圆心为D，⊙O的切线为RQ。求∠RQS的大小。 | As shown in the diagram, the measure of ⌒DQS is 238, D is the center of ⊙D, the tangent to ⊙D is RQ. Find the measure of ∠RQS. | 408.png | [
"Shape(QS,DSQ)",
"Shape(SQ,QD,DS)",
"Shape(SD,DQ,DQT,DTS)",
"Shape(RQ,QS)",
"Collinear(QR)",
"Cocircular(D,SQT)"
] | [
"Equal(MeasureOfArc(DQS),238)",
"IsCentreOfCircle(D,D)",
"IsTangentOfCircle(RQ,D)"
] | [
"Equal(MeasureOfArc(DQS),238)",
"IsCentreOfCircle(D,D)",
"IsTangentOfCircle(RQ,D)"
] | Value(MeasureOfAngle(RQS)) | 61 | [
"arc_property_center_angle(1,DQS,D)",
"round_angle(1,QDS,SDQ)",
"radius_of_circle_property_length_equal(1,DS,D)",
"radius_of_circle_property_length_equal(1,DQ,D)",
"isosceles_triangle_judgment_line_equal(1,DSQ)",
"isosceles_triangle_property_angle_equal(1,DSQ)",
"triangle_property_angle_sum(1,DSQ)",
"... | {"START": ["arc_property_center_angle(1,DQS,D)", "round_angle(1,QDS,SDQ)", "radius_of_circle_property_length_equal(1,DS,D)", "radius_of_circle_property_length_equal(1,DQ,D)", "triangle_property_angle_sum(1,DSQ)", "tangent_of_circle_property_perpendicular(2,RQ,D,D)", "angle_addition(1,RQS,SQD)"], "isosceles_triangle_jud... | |
409 | NaZhu_2023-03-12 | Geometry3k-417 | 1 | 如图所示，AC=5，BA=12，CB=x，∠BAC=60°。求x的值。 | As shown in the diagram, AC=5, BA=12, CB=x, ∠BAC=60°. Find the value of x. | 409.png | [
"Shape(CB,BA,AC)"
] | [
"Equal(LengthOfLine(AC),5)",
"Equal(LengthOfLine(BA),12)",
"Equal(LengthOfLine(CB),x)",
"Equal(MeasureOfAngle(BAC),60)"
] | [
"Equal(LengthOfLine(AC),5)",
"Equal(LengthOfLine(BA),12)",
"Equal(LengthOfLine(CB),x)",
"Equal(MeasureOfAngle(BAC),60)"
] | Value(x) | sqrt(109) | [
"cosine_theorem(1,ACB)"
] | {"START": ["cosine_theorem(1,ACB)"]} | |
410 | NaZhu_2023-03-12 | Geometry3k-418 | 5 | 如图所示，BA=y，BF=x，FA=z，LA=sqrt(3)，LF=2*sqrt(3)，FB⊥AB，LA⊥FA。求x的值。 | As shown in the diagram, BA=y, BF=x, FA=z, LA=sqrt(3), LF=2*sqrt(3), FB⊥AB, LA⊥FA. Find the value of x. | 410.png | [
"Shape(FB,BA,AF)",
"Shape(BL,LA,AB)",
"Collinear(LBF)"
] | [
"Equal(LengthOfLine(BA),y)",
"Equal(LengthOfLine(BF),x)",
"Equal(LengthOfLine(FA),z)",
"Equal(LengthOfLine(LA),sqrt(3))",
"Equal(LengthOfLine(LF),2*sqrt(3))",
"PerpendicularBetweenLine(FB,AB)",
"PerpendicularBetweenLine(LA,FA)"
] | [
"Equal(LengthOfLine(BA),y)",
"Equal(LengthOfLine(BF),x)",
"Equal(LengthOfLine(FA),z)",
"Equal(LengthOfLine(LA),sqrt(3))",
"Equal(LengthOfLine(LF),2*sqrt(3))",
"PerpendicularBetweenLine(FB,AB)",
"PerpendicularBetweenLine(LA,FA)"
] | Value(x) | 3*sqrt(3)/2 | [
"adjacent_complementary_angle(1,FBA,ABL)",
"mirror_similar_triangle_judgment_aa(1,ABL,FLA)",
"mirror_similar_triangle_property_line_ratio(1,ABL,FLA)",
"mirror_similar_triangle_property_line_ratio(1,BLA,AFL)",
"line_addition(1,LB,BF)"
] | {"START": ["adjacent_complementary_angle(1,FBA,ABL)", "line_addition(1,LB,BF)"], "adjacent_complementary_angle(1,FBA,ABL)": ["mirror_similar_triangle_judgment_aa(1,ABL,FLA)"], "mirror_similar_triangle_judgment_aa(1,ABL,FLA)": ["mirror_similar_triangle_property_line_ratio(1,ABL,FLA)", "mirror_similar_triangle_property_l... | |
411 | NaZhu_2023-03-12 | Geometry3k-419 | 2 | 如图所示，AB=x，AC=16，CB=30，BC垂直于AC。求x的值。 | As shown in the diagram, AB=x, AC=16, CB=30, BC⊥AC. Find the value of x. | 411.png | [
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(AB),x)",
"Equal(LengthOfLine(AC),16)",
"Equal(LengthOfLine(CB),30)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(AB),x)",
"Equal(LengthOfLine(AC),16)",
"Equal(LengthOfLine(CB),30)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(x) | 34 | [
"right_triangle_judgment_angle(1,BCA)",
"right_triangle_property_pythagorean(1,BCA)"
] | {"START": ["right_triangle_judgment_angle(1,BCA)"], "right_triangle_judgment_angle(1,BCA)": ["right_triangle_property_pythagorean(1,BCA)"]} | |
412 | JiaZou_2023-04-09 | Geometry3k-420 | 3 | 如图所示，∠POM=43°，FB平行于QM，KC∥GJ。求∠BPO的大小。 | As shown in the diagram, ∠POM=43°, FB∥QM, KC∥GJ. Find the measure of ∠BPO. | 412.png | [
"Shape(KP,PB)",
"Shape(BP,PO)",
"Shape(PO,OM)",
"Shape(MO,OC)",
"Shape(KP,PH)",
"Shape(GH,HP)",
"Shape(PH,HN,NO,OP)",
"Shape(CO,ON)",
"Shape(ON,NJ)",
"Shape(FH,HG)",
"Shape(NH,HF)",
"Shape(QN,NH)",
"Shape(JN,NQ)",
"Collinear(KPOC)",
"Collinear(GHNJ)",
"Collinear(BPHF)",
"Collinear(MO... | [
"Equal(MeasureOfAngle(POM),43)",
"ParallelBetweenLine(FB,QM)",
"ParallelBetweenLine(KC,GJ)"
] | [
"Equal(MeasureOfAngle(POM),43)",
"ParallelBetweenLine(FB,QM)",
"ParallelBetweenLine(KC,GJ)"
] | Value(MeasureOfAngle(BPO)) | 137 | [
"parallel_property_collinear_extend(3,FB,QM,P)",
"parallel_property_collinear_extend(3,MQ,BP,O)",
"parallel_property_ipsilateral_internal_angle(1,PB,OM)"
] | {"START": ["parallel_property_collinear_extend(3,FB,QM,P)"], "parallel_property_collinear_extend(3,FB,QM,P)": ["parallel_property_collinear_extend(3,MQ,BP,O)"], "parallel_property_collinear_extend(3,MQ,BP,O)": ["parallel_property_ipsilateral_internal_angle(1,PB,OM)"]} | |
413 | JiaZou_2023-04-09 | Geometry3k-421 | 1 | 如图所示，YX=24，ZY=28，∠XWZ=105°，WX和ZY是平行四边形WZYX的一组对边。求直线WZ的长度。 | As shown in the diagram, YX=24, ZY=28, ∠XWZ=105°, WX and ZY are opposite sides of the parallelogram WZYX. Find the length of line WZ. | 413.png | [
"Shape(WZ,ZY,YX,XW)"
] | [
"Equal(LengthOfLine(YX),24)",
"Equal(LengthOfLine(ZY),28)",
"Equal(MeasureOfAngle(XWZ),105)",
"Parallelogram(WZYX)"
] | [
"Equal(LengthOfLine(YX),24)",
"Equal(LengthOfLine(ZY),28)",
"Equal(MeasureOfAngle(XWZ),105)"
] | Value(LengthOfLine(WZ)) | 24 | [
"parallelogram_property_opposite_line_equal(1,WZYX)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,WZYX)"]} | |
414 | JiaZou_2023-04-09 | Geometry3k-422 | 1 | 如图所示，BC=4*x-17，DF=2*x-1，∠CBF=3*y+5°，∠DFB=5*y-13°，DB和FC是平行四边形BDFC的一组对边。求y的值。 | As shown in the diagram, BC=4*x-17, DF=2*x-1, ∠CBF=3*y+5°, ∠DFB=5*y-13°, DB and FC are opposite sides of the parallelogram BDFC. Find the value of y. | 414.png | [
"Shape(BD,DF,FB)",
"Shape(FC,CB,BF)"
] | [
"Equal(LengthOfLine(BC),4*x-17)",
"Equal(LengthOfLine(DF),2*x-1)",
"Equal(MeasureOfAngle(CBF),3*y+5)",
"Equal(MeasureOfAngle(DFB),5*y-13)",
"Parallelogram(BDFC)"
] | [
"Equal(LengthOfLine(BC),4*x-17)",
"Equal(LengthOfLine(DF),2*x-1)",
"Equal(MeasureOfAngle(CBF),3*y+5)",
"Equal(MeasureOfAngle(DFB),5*y-13)"
] | Value(y) | 9 | [
"parallel_property_alternate_interior_angle(1,BC,DF)"
] | {"START": ["parallel_property_alternate_interior_angle(1,BC,DF)"]} | |
415 | JiaZou_2023-04-09 | Geometry3k-423 | 5 | 如图所示，AC=21，AD=17，DE=8，四边形BCAD是平行四边形，CA垂直于EA，DE⊥AE。求BCAD的面积。 | As shown in the diagram, AC=21, AD=17, DE=8, quadrilateral BCAD is a parallelogram, CA is perpendicular to EA, DE⊥AE. Find the area of quadrilateral BCAD. | 415.png | [
"Shape(BC,CA,AE,EB)",
"Shape(EA,AD,DE)",
"Collinear(BED)"
] | [
"Equal(LengthOfLine(AC),21)",
"Equal(LengthOfLine(AD),17)",
"Equal(LengthOfLine(DE),8)",
"Parallelogram(BCAD)",
"PerpendicularBetweenLine(CA,EA)",
"PerpendicularBetweenLine(DE,AE)"
] | [
"Equal(LengthOfLine(AC),21)",
"Equal(LengthOfLine(AD),17)",
"Equal(LengthOfLine(DE),8)",
"PerpendicularBetweenLine(CA,EA)",
"PerpendicularBetweenLine(DE,AE)"
] | Value(AreaOfQuadrilateral(BCAD)) | 315 | [
"right_triangle_judgment_angle(1,DEA)",
"right_triangle_property_pythagorean(1,DEA)",
"altitude_of_quadrilateral_judgment_left_vertex(1,AE,ADBC)",
"parallelogram_property_opposite_line_equal(1,DBCA)",
"parallelogram_area_formula_common(1,ADBC)"
] | {"START": ["right_triangle_judgment_angle(1,DEA)", "altitude_of_quadrilateral_judgment_left_vertex(1,AE,ADBC)", "parallelogram_property_opposite_line_equal(1,DBCA)", "parallelogram_area_formula_common(1,ADBC)"], "right_triangle_judgment_angle(1,DEA)": ["right_triangle_property_pythagorean(1,DEA)"]} | |
416 | JiaZou_2023-04-09 | Geometry3k-424 | 7 | 如图所示，JN=14-x，KL=3*x+2*y，MK=6*x，LJMK是平行四边形，四边形PNML是长方形。求y的值。 | As shown in the diagram, JN=14-x, KL=3*x+2*y, MK=6*x, quadrilateral LJMK is a parallelogram, quadrilateral PNML is a rectangle. Find the value of y. | 416.png | [
"Shape(PN,NJ,JP)",
"Shape(JN,NM,MJ)",
"Shape(JM,ML,LJ)",
"Shape(JL,LP,PJ)",
"Shape(MK,KL,LM)",
"Collinear(PJM)",
"Collinear(NJL)"
] | [
"Equal(LengthOfLine(JN),14-x)",
"Equal(LengthOfLine(KL),3*x+2*y)",
"Equal(LengthOfLine(MK),6*x)",
"Parallelogram(LJMK)",
"Rectangle(PNML)"
] | [
"Equal(LengthOfLine(JN),14-x)",
"Equal(LengthOfLine(KL),3*x+2*y)",
"Equal(LengthOfLine(MK),6*x)"
] | Value(y) | 3 | [
"line_addition(1,PJ,JM)",
"line_addition(1,NJ,JL)",
"rectangle_property_diagonal_equal(1,PNML)",
"parallelogram_property_diagonal_bisection(1,PNML,J)",
"parallelogram_property_diagonal_bisection(1,NMLP,J)",
"parallelogram_property_opposite_line_equal(1,LJMK)",
"parallelogram_property_opposite_line_equal... | {"START": ["line_addition(1,PJ,JM)", "line_addition(1,NJ,JL)", "rectangle_property_diagonal_equal(1,PNML)", "parallelogram_property_diagonal_bisection(1,PNML,J)", "parallelogram_property_diagonal_bisection(1,NMLP,J)", "parallelogram_property_opposite_line_equal(1,LJMK)", "parallelogram_property_opposite_line_equal(1,JM... | |
417 | JiaZou_2023-04-09 | Geometry3k-425 | 2 | 如图所示，∠EDF=39°，∠FBA=48°，FC∥ED，AF⊥BF，DC⊥FC，FE⊥DE。求∠FDC的大小。 | As shown in the diagram, ∠EDF=39°, ∠FBA=48°, FC∥ED, AF is perpendicular to BF, DC⊥FC, FE is perpendicular to DE. Find the measure of ∠FDC. | 417.png | [
"Shape(AF,FB,BA)",
"Shape(FE,ED,DF)",
"Shape(FD,DC,CB,BF)",
"Collinear(FBC)",
"Collinear(AFE)"
] | [
"Equal(MeasureOfAngle(EDF),39)",
"Equal(MeasureOfAngle(FBA),48)",
"ParallelBetweenLine(FC,ED)",
"PerpendicularBetweenLine(AF,BF)",
"PerpendicularBetweenLine(DC,FC)",
"PerpendicularBetweenLine(FE,DE)"
] | [
"Equal(MeasureOfAngle(EDF),39)",
"Equal(MeasureOfAngle(FBA),48)",
"ParallelBetweenLine(FC,ED)",
"PerpendicularBetweenLine(AF,BF)",
"PerpendicularBetweenLine(DC,FC)",
"PerpendicularBetweenLine(FE,DE)"
] | Value(MeasureOfAngle(FDC)) | 51 | [
"parallel_property_alternate_interior_angle(1,FC,ED)",
"triangle_property_angle_sum(1,FDC)"
] | {"START": ["parallel_property_alternate_interior_angle(1,FC,ED)", "triangle_property_angle_sum(1,FDC)"]} | |
418 | NaZhu_2023-03-12 | Geometry3k-426 | 6 | 如图所示，AN=21，BL=6，BN=18，SC=4，BL垂直于NL，SC⊥NC。求△SBN的面积与△NBA的面积之和。 | As shown in the diagram, AN=21, BL=6, BN=18, SC=4, BL is perpendicular to NL, SC⊥NC. Find the sum of the area of triangle SBN and the area of triangle NBA. | 418.png | [
"Shape(BA,AL,LB)",
"Shape(BL,LN,NB)",
"Shape(SB,BC,CS)",
"Shape(SC,CN,NS)",
"Collinear(ALN)",
"Collinear(BCN)"
] | [
"Equal(LengthOfLine(AN),21)",
"Equal(LengthOfLine(BL),6)",
"Equal(LengthOfLine(BN),18)",
"Equal(LengthOfLine(SC),4)",
"PerpendicularBetweenLine(BL,NL)",
"PerpendicularBetweenLine(SC,NC)"
] | [
"Equal(LengthOfLine(AN),21)",
"Equal(LengthOfLine(BL),6)",
"Equal(LengthOfLine(BN),18)",
"Equal(LengthOfLine(SC),4)",
"PerpendicularBetweenLine(BL,NL)",
"PerpendicularBetweenLine(SC,NC)"
] | Value(Add(AreaOfTriangle(SBN),AreaOfTriangle(NBA))) | 99 | [
"adjacent_complementary_angle(1,ALB,BLN)",
"adjacent_complementary_angle(1,BCS,SCN)",
"altitude_of_triangle_judgment(1,BL,BAN)",
"altitude_of_triangle_judgment(1,SC,SBN)",
"triangle_area_formula_common(1,BAN)",
"triangle_area_formula_common(1,SBN)"
] | {"START": ["adjacent_complementary_angle(1,ALB,BLN)", "adjacent_complementary_angle(1,BCS,SCN)", "triangle_area_formula_common(1,BAN)", "triangle_area_formula_common(1,SBN)"], "adjacent_complementary_angle(1,ALB,BLN)": ["altitude_of_triangle_judgment(1,BL,BAN)"], "adjacent_complementary_angle(1,BCS,SCN)": ["altitude_of... | |
419 | JiaZou_2023-04-09 | Geometry3k-427 | 9 | 如图所示，RD=3，SA=3，TA=x，UC=x，四边形TSRU的周长为18，RC是⊙O的切线，圆O的切线为RD，SA是⊙O的切线，⊙O的切线为SD，圆O的切线为TA，TB是⊙O的切线，UB是圆O的切线，⊙O的切线为UC。求x的值。 | As shown in the diagram, RD=3, SA=3, TA=x, UC=x, the perimeter of quadrilateral TSRU is 18, RC is the tangent to ⊙J, RD is the tangent to circle J, SA is the tangent to ⊙J, the tangent to ⊙J is SD, TA is the tangent to circle J, the tangent to circle J is TB, the tangent to ⊙J is UB, UC is the tangent to ⊙J. Find the v... | 419.png | [
"Shape(BT,TA,JBA)",
"Shape(AS,SD,JAD)",
"Shape(DR,RC,JDC)",
"Shape(CU,UB,JCB)",
"Shape(JAD,JDC,JCB,JBA)",
"Collinear(TBU)",
"Collinear(TAS)",
"Collinear(SDR)",
"Collinear(UCR)",
"Cocircular(J,BADC)"
] | [
"Equal(LengthOfLine(RD),3)",
"Equal(LengthOfLine(SA),3)",
"Equal(LengthOfLine(TA),x)",
"Equal(LengthOfLine(UC),x)",
"Equal(PerimeterOfQuadrilateral(TSRU),18)",
"IsTangentOfCircle(RC,J)",
"IsTangentOfCircle(RD,J)",
"IsTangentOfCircle(SA,J)",
"IsTangentOfCircle(SD,J)",
"IsTangentOfCircle(TA,J)",
"... | [
"Equal(LengthOfLine(RD),3)",
"Equal(LengthOfLine(SA),3)",
"Equal(LengthOfLine(TA),x)",
"Equal(LengthOfLine(UC),x)",
"Equal(PerimeterOfQuadrilateral(TSRU),18)",
"IsTangentOfCircle(RC,J)",
"IsTangentOfCircle(RD,J)",
"IsTangentOfCircle(SA,J)",
"IsTangentOfCircle(SD,J)",
"IsTangentOfCircle(TA,J)",
"... | Value(x) | 3/2 | [
"tangent_of_circle_property_length_equal(1,SA,SD,J)",
"tangent_of_circle_property_length_equal(1,TB,TA,J)",
"tangent_of_circle_property_length_equal(1,UC,UB,J)",
"tangent_of_circle_property_length_equal(1,RD,RC,J)",
"line_addition(1,TB,BU)",
"line_addition(1,TA,AS)",
"line_addition(1,SD,DR)",
"line_ad... | {"START": ["tangent_of_circle_property_length_equal(1,SA,SD,J)", "tangent_of_circle_property_length_equal(1,TB,TA,J)", "tangent_of_circle_property_length_equal(1,UC,UB,J)", "tangent_of_circle_property_length_equal(1,RD,RC,J)", "line_addition(1,TB,BU)", "line_addition(1,TA,AS)", "line_addition(1,SD,DR)", "line_addition(... | |
420 | JiaZou_2023-04-09 | Geometry3k-428 | 18 | 如图所示，AB=24，BC=8，∠ADC=45°，∠CBA=60°，AB∥DC，BF⊥CF，DE⊥AE。求四边形ADCB的周长。 | As shown in the diagram, AB=24, BC=8, ∠ADC=45°, ∠CBA=60°, AB is parallel to DC, BF⊥CF, DE is perpendicular to AE. Find the perimeter of quadrilateral ADCB. | 420.png | [
"Shape(AD,DE,EA)",
"Shape(AE,EC,CF,FA)",
"Shape(CB,BF,FC)",
"Collinear(AFB)",
"Collinear(DEC)"
] | [
"Equal(LengthOfLine(AB),24)",
"Equal(LengthOfLine(BC),8)",
"Equal(MeasureOfAngle(ADC),45)",
"Equal(MeasureOfAngle(CBA),60)",
"ParallelBetweenLine(AB,DC)",
"PerpendicularBetweenLine(BF,CF)",
"PerpendicularBetweenLine(DE,AE)"
] | [
"Equal(LengthOfLine(AB),24)",
"Equal(LengthOfLine(BC),8)",
"Equal(MeasureOfAngle(ADC),45)",
"Equal(MeasureOfAngle(CBA),60)",
"ParallelBetweenLine(AB,DC)",
"PerpendicularBetweenLine(BF,CF)",
"PerpendicularBetweenLine(DE,AE)"
] | Value(PerimeterOfQuadrilateral(ADCB)) | 4*sqrt(3)+4*sqrt(6)+52 | [
"adjacent_complementary_angle(1,BFC,CFA)",
"adjacent_complementary_angle(1,DEA,AEC)",
"parallel_property_collinear_extend(3,AB,DC,F)",
"parallel_property_collinear_extend(3,CD,FA,E)",
"parallel_property_ipsilateral_internal_angle(1,CE,FA)",
"parallel_judgment_ipsilateral_internal_angle(1,EA,CF)",
"paral... | {"START": ["adjacent_complementary_angle(1,BFC,CFA)", "adjacent_complementary_angle(1,DEA,AEC)", "parallel_property_collinear_extend(3,AB,DC,F)", "triangle_property_angle_sum(1,ADE)", "triangle_property_angle_sum(1,BFC)", "sine_theorem(1,CBF)", "sine_theorem(1,BFC)", "sine_theorem(1,ADE)", "sine_theorem(1,EAD)", "line_... | |
421 | JiaZou_2023-04-09 | Geometry3k-429 | 2 | 如图所示，AB=3，⊙B的圆心为B。求圆B的周长。 | As shown in the diagram, AB=3, B is the center of circle B. Find the circumference of the ⊙B. | 421.png | [
"Shape(BA)",
"Cocircular(B,A)"
] | [
"Equal(LengthOfLine(AB),3)",
"IsCentreOfCircle(B,B)"
] | [
"Equal(LengthOfLine(AB),3)",
"IsCentreOfCircle(B,B)"
] | Value(PerimeterOfCircle(B)) | 6*pi | [
"radius_of_circle_property_length_equal(1,BA,B)",
"circle_perimeter_formula(1,B)"
] | {"START": ["radius_of_circle_property_length_equal(1,BA,B)", "circle_perimeter_formula(1,B)"]} | |
422 | NaZhu_2023-03-12 | Geometry3k-430 | 2 | 如图所示，AC=x，BA=18，∠ABC=25°，CA垂直于BA。求x的值。 | As shown in the diagram, AC=x, BA=18, ∠ABC=25°, CA⊥BA. Find the value of x. | 422.png | [
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BA),18)",
"Equal(MeasureOfAngle(ABC),25)",
"PerpendicularBetweenLine(CA,BA)"
] | [
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BA),18)",
"Equal(MeasureOfAngle(ABC),25)",
"PerpendicularBetweenLine(CA,BA)"
] | Value(x) | 18*tan(5*pi/36) | [
"triangle_property_angle_sum(1,ABC)",
"sine_theorem(1,ABC)"
] | {"START": ["triangle_property_angle_sum(1,ABC)", "sine_theorem(1,ABC)"]} | |
423 | JiaZou_2023-04-09 | Geometry3k-431 | 1 | 如图所示，EH=9，HG=15，∠EHD=45°，EF和HG是▱EHGF的一组对边，ED⊥GD。求四边形EHGF的面积。 | As shown in the diagram, EH=9, HG=15, ∠EHD=45°, EHGF is a parallelogram, ED⊥GD. Find the area of EHGF. | 423.png | [
"Shape(EH,HD,DE)",
"Shape(ED,DG,GF,FE)",
"Collinear(HDG)"
] | [
"Equal(LengthOfLine(EH),9)",
"Equal(LengthOfLine(HG),15)",
"Equal(MeasureOfAngle(EHD),45)",
"Parallelogram(EHGF)",
"PerpendicularBetweenLine(ED,GD)"
] | [
"Equal(LengthOfLine(EH),9)",
"Equal(LengthOfLine(HG),15)",
"Equal(MeasureOfAngle(EHD),45)",
"PerpendicularBetweenLine(ED,GD)"
] | Value(AreaOfQuadrilateral(EHGF)) | 135*sqrt(2)/2 | [
"parallelogram_area_formula_sine(1,EHGF)"
] | {"START": ["parallelogram_area_formula_sine(1,EHGF)"]} | |
424 | JiaZou_2023-04-09 | Geometry3k-432 | 6 | 如图所示，∠ADG=36°，∠AGF=104°，∠EFC=40°，AB垂直于CB。求∠BCF的大小。 | As shown in the diagram, ∠ADG=36°, ∠AGF=104°, ∠EFC=40°, AB⊥CB. Find the measure of ∠BCF. | 424.png | [
"Shape(AD,DG,GA)",
"Shape(FG,GB,BF)",
"Shape(FB,BC,CF)",
"Shape(AG,GF)",
"Shape(EF,FC)",
"Shape(BG,GD)",
"Collinear(DGFC)",
"Collinear(AGB)",
"Collinear(BFE)"
] | [
"Equal(MeasureOfAngle(ADG),36)",
"Equal(MeasureOfAngle(AGF),104)",
"Equal(MeasureOfAngle(EFC),40)",
"PerpendicularBetweenLine(AB,CB)"
] | [
"Equal(MeasureOfAngle(ADG),36)",
"Equal(MeasureOfAngle(AGF),104)",
"Equal(MeasureOfAngle(EFC),40)",
"PerpendicularBetweenLine(AB,CB)"
] | Value(MeasureOfAngle(BCF)) | 14 | [
"vertical_angle(1,EFC,BFG)",
"adjacent_complementary_angle(1,AGF,FGB)",
"adjacent_complementary_angle(1,EFC,CFB)",
"triangle_property_angle_sum(1,FGB)",
"triangle_property_angle_sum(1,CFB)",
"angle_addition(1,GBF,FBC)"
] | {"START": ["vertical_angle(1,EFC,BFG)", "adjacent_complementary_angle(1,AGF,FGB)", "adjacent_complementary_angle(1,EFC,CFB)", "triangle_property_angle_sum(1,FGB)", "triangle_property_angle_sum(1,CFB)", "angle_addition(1,GBF,FBC)"]} | |
425 | JiaZou_2023-04-09 | Geometry3k-433 | 4 | 如图所示，PT=6，QR=12，SP=4，PT平行于QR。求直线SQ的长度。 | As shown in the diagram, PT=6, QR=12, SP=4, PT∥QR. Find the length of line SQ. | 425.png | [
"Shape(SP,PT,TS)",
"Shape(PQ,QR,RT,TP)",
"Collinear(SPQ)",
"Collinear(STR)"
] | [
"Equal(LengthOfLine(PT),6)",
"Equal(LengthOfLine(QR),12)",
"Equal(LengthOfLine(SP),4)",
"ParallelBetweenLine(PT,QR)"
] | [
"Equal(LengthOfLine(PT),6)",
"Equal(LengthOfLine(QR),12)",
"Equal(LengthOfLine(SP),4)",
"ParallelBetweenLine(PT,QR)"
] | Value(LengthOfLine(SQ)) | 8 | [
"parallel_property_corresponding_angle(1,PT,QR,S)",
"similar_triangle_judgment_aa(1,TSP,RSQ)",
"similar_triangle_property_line_ratio(1,TSP,RSQ)",
"similar_triangle_property_line_ratio(1,SPT,SQR)"
] | {"START": ["parallel_property_corresponding_angle(1,PT,QR,S)"], "parallel_property_corresponding_angle(1,PT,QR,S)": ["similar_triangle_judgment_aa(1,TSP,RSQ)"], "similar_triangle_judgment_aa(1,TSP,RSQ)": ["similar_triangle_property_line_ratio(1,TSP,RSQ)", "similar_triangle_property_line_ratio(1,SPT,SQR)"]} | |
426 | JiaZou_2023-04-09 | Geometry3k-434 | 1 | 如图所示，∠BEC=2*x°，∠BFA=3*x-15°，∠ECB=y**2°，∠FAE=68°，AF平行于EB。求x的值。 | As shown in the diagram, ∠BEC=2*x°, ∠BFA=3*x-15°, ∠ECB=y**2°, ∠FAE=68°, AF is parallel to EB. Find the value of x. | 426.png | [
"Shape(FA,AE,EB,BF)",
"Shape(BE,EC,CB)",
"Collinear(FBC)",
"Collinear(AEC)"
] | [
"Equal(MeasureOfAngle(BEC),2*x)",
"Equal(MeasureOfAngle(BFA),3*x-15)",
"Equal(MeasureOfAngle(ECB),y**2)",
"Equal(MeasureOfAngle(FAE),68)",
"ParallelBetweenLine(AF,EB)"
] | [
"Equal(MeasureOfAngle(BEC),2*x)",
"Equal(MeasureOfAngle(BFA),3*x-15)",
"Equal(MeasureOfAngle(ECB),y**2)",
"Equal(MeasureOfAngle(FAE),68)",
"ParallelBetweenLine(AF,EB)"
] | Value(x) | 34 | [
"parallel_property_corresponding_angle(2,AF,EB,C)"
] | {"START": ["parallel_property_corresponding_angle(2,AF,EB,C)"]} | |
427 | NaZhu_2023-03-12 | Geometry3k-435 | 15 | 如图所示，AB=6，AF=8，BC=x，CD=y，DE=2*y-3，FE=x+10/3，BF∥CD，CB∥DF。求直线CD的长度。 | As shown in the diagram, AB=6, AF=8, BC=x, CD=y, DE=2*y-3, FE=x+10/3, BF is parallel to CD, CB∥DF. Find the length of line CD. | 427.png | [
"Shape(AB,BF,FA)",
"Shape(BC,CD,DF,FB)",
"Shape(FD,DE,EF)",
"Collinear(ABC)",
"Collinear(CDE)",
"Collinear(AFE)"
] | [
"Equal(LengthOfLine(AB),6)",
"Equal(LengthOfLine(AF),8)",
"Equal(LengthOfLine(BC),x)",
"Equal(LengthOfLine(CD),y)",
"Equal(LengthOfLine(DE),2*y-3)",
"Equal(LengthOfLine(FE),x+10/3)",
"ParallelBetweenLine(BF,CD)",
"ParallelBetweenLine(CB,DF)"
] | [
"ParallelBetweenLine(BF,CD)",
"ParallelBetweenLine(CB,DF)"
] | Value(LengthOfLine(CD)) | 9 | [
"line_addition(1,AB,BC)",
"line_addition(1,CD,DE)",
"line_addition(1,AF,FE)",
"parallel_property_ipsilateral_internal_angle(1,BF,CD)",
"parallel_property_ipsilateral_internal_angle(1,CB,DF)",
"flat_angle(1,ABC)",
"flat_angle(1,CDE)",
"angle_addition(1,ABF,FBC)",
"angle_addition(1,CDF,FDE)",
"simil... | {"START": ["line_addition(1,AB,BC)", "line_addition(1,CD,DE)", "line_addition(1,AF,FE)", "parallel_property_ipsilateral_internal_angle(1,BF,CD)", "parallel_property_ipsilateral_internal_angle(1,CB,DF)", "flat_angle(1,ABC)", "flat_angle(1,CDE)", "angle_addition(1,ABF,FBC)", "angle_addition(1,CDF,FDE)"], "angle_addition(... | |
428 | NaZhu_2023-03-12 | Geometry3k-436 | 1 | 如图所示，PS=RS，∠QSR=48°，∠SQP=∠RQS，QP垂直于SP，SR⊥QR。求∠SQP的大小。 | As shown in the diagram, PS=RS, ∠QSR=48°, ∠SQP=∠RQS, QP is perpendicular to SP, SR⊥QR. Find the measure of ∠SQP. | 428.png | [
"Shape(QP,PS,SQ)",
"Shape(QS,SR,RQ)"
] | [
"Equal(LengthOfLine(PS),LengthOfLine(RS))",
"Equal(MeasureOfAngle(QSR),48)",
"Equal(MeasureOfAngle(SQP),MeasureOfAngle(RQS))",
"PerpendicularBetweenLine(QP,SP)",
"PerpendicularBetweenLine(SR,QR)"
] | [
"Equal(LengthOfLine(PS),LengthOfLine(RS))",
"Equal(MeasureOfAngle(QSR),48)",
"Equal(MeasureOfAngle(SQP),MeasureOfAngle(RQS))",
"PerpendicularBetweenLine(QP,SP)",
"PerpendicularBetweenLine(SR,QR)"
] | Value(MeasureOfAngle(SQP)) | 42 | [
"triangle_property_angle_sum(1,QSR)"
] | {"START": ["triangle_property_angle_sum(1,QSR)"]} | |
429 | JiaZou_2023-04-09 | Geometry3k-437 | 9 | 如图所示，Add(PerimeterOfCircle(K)=PerimeterOfCircle(J)，CJ=2*x，HA=x，HC=x，KA=4*x，⊙H的圆心为H，J是圆J的圆心，圆K的圆心为K。求直线KJ的长度。 | As shown in the diagram, Add(PerimeterOfCircle(K)=PerimeterOfCircle(J), CJ=2*x, HA=x, HC=x, KA=4*x, H is the center of circle H, the center of ⊙J is J, the center of ⊙K is K. Find the length of line KJ. | 429.png | [
"Shape(KA,KAB,BK)",
"Shape(AK,KB,KBA)",
"Shape(KBA,JBC,HCA)",
"Shape(CH,HA,HAC)",
"Shape(HC,HCA,AH)",
"Shape(BJ,JC,JCB)",
"Shape(CJ,JB,JBC)",
"Collinear(KAH)",
"Collinear(HCJ)",
"Collinear(KBJ)",
"Cocircular(K,BA)",
"Cocircular(J,CB)",
"Cocircular(H,AC)"
] | [
"Equal(Add(PerimeterOfCircle(K),PerimeterOfCircle(J),PerimeterOfCircle(H)),56*pi)",
"Equal(LengthOfLine(CJ),2*x)",
"Equal(LengthOfLine(HA),x)",
"Equal(LengthOfLine(HC),x)",
"Equal(LengthOfLine(KA),4*x)",
"IsCentreOfCircle(H,H)",
"IsCentreOfCircle(J,J)",
"IsCentreOfCircle(K,K)"
] | [
"Equal(Add(PerimeterOfCircle(K),PerimeterOfCircle(J),PerimeterOfCircle(H)),56*pi)",
"Equal(LengthOfLine(CJ),2*x)",
"Equal(LengthOfLine(HA),x)",
"Equal(LengthOfLine(HC),x)",
"Equal(LengthOfLine(KA),4*x)",
"IsCentreOfCircle(H,H)",
"IsCentreOfCircle(J,J)",
"IsCentreOfCircle(K,K)"
] | Value(LengthOfLine(KJ)) | 24 | [
"radius_of_circle_property_length_equal(1,KA,K)",
"radius_of_circle_property_length_equal(1,KB,K)",
"radius_of_circle_property_length_equal(1,HC,H)",
"radius_of_circle_property_length_equal(1,JC,J)",
"radius_of_circle_property_length_equal(1,JB,J)",
"circle_perimeter_formula(1,K)",
"circle_perimeter_for... | {"START": ["radius_of_circle_property_length_equal(1,KA,K)", "radius_of_circle_property_length_equal(1,KB,K)", "radius_of_circle_property_length_equal(1,HC,H)", "radius_of_circle_property_length_equal(1,JC,J)", "radius_of_circle_property_length_equal(1,JB,J)", "circle_perimeter_formula(1,K)", "circle_perimeter_formula(... | |
430 | NaZhu_2023-03-12 | Geometry3k-438 | 3 | 如图所示，∠CBA=17°，∠DCA=29°，AC⊥CC。求∠BAC的大小。 | As shown in the diagram, ∠CBA=17°, ∠DCA=29°, AC⊥CC. Find the measure of ∠BAC. | 430.png | [
"Shape(AD,DC,CA)",
"Shape(AC,CB,BA)",
"Collinear(DCB)"
] | [
"Equal(MeasureOfAngle(CBA),17)",
"Equal(MeasureOfAngle(DCA),29)",
"PerpendicularBetweenLine(AC,CD)"
] | [
"Equal(MeasureOfAngle(CBA),17)",
"Equal(MeasureOfAngle(DCA),29)",
"PerpendicularBetweenLine(AC,CD)"
] | Value(MeasureOfAngle(BAC)) | 12 | [
"flat_angle(1,DCB)",
"triangle_property_angle_sum(1,ACB)",
"angle_addition(1,DCA,ACB)"
] | {"START": ["flat_angle(1,DCB)", "triangle_property_angle_sum(1,ACB)", "angle_addition(1,DCA,ACB)"]} | |
431 | NaZhu_2023-03-12 | Geometry3k-439 | 3 | 如图所示，AC=12，AS=x，BC=9，SB=7，SR=6，RC⊥BC，RS⊥AS。求直线AS的长度。 | As shown in the diagram, AC=12, AS=x, BC=9, SB=7, SR=6, RC is perpendicular to BC, RS⊥AS. Find the length of line AS. | 431.png | [
"Shape(AR,RS,SA)",
"Shape(SR,RC,CB,BS)",
"Collinear(ARC)",
"Collinear(ASB)"
] | [
"Equal(LengthOfLine(AC),12)",
"Equal(LengthOfLine(AS),x)",
"Equal(LengthOfLine(BC),9)",
"Equal(LengthOfLine(SB),7)",
"Equal(LengthOfLine(SR),6)",
"PerpendicularBetweenLine(RC,BC)",
"PerpendicularBetweenLine(RS,AS)"
] | [
"Equal(LengthOfLine(AC),12)",
"Equal(LengthOfLine(AS),x)",
"Equal(LengthOfLine(BC),9)",
"Equal(LengthOfLine(SB),7)",
"Equal(LengthOfLine(SR),6)",
"PerpendicularBetweenLine(RC,BC)",
"PerpendicularBetweenLine(RS,AS)"
] | Value(LengthOfLine(AS)) | 8 | [
"mirror_similar_triangle_judgment_aa(1,RSA,BAC)",
"mirror_similar_triangle_property_line_ratio(1,RSA,BAC)",
"mirror_similar_triangle_property_line_ratio(1,ARS,ACB)"
] | {"START": ["mirror_similar_triangle_judgment_aa(1,RSA,BAC)"], "mirror_similar_triangle_judgment_aa(1,RSA,BAC)": ["mirror_similar_triangle_property_line_ratio(1,RSA,BAC)", "mirror_similar_triangle_property_line_ratio(1,ARS,ACB)"]} | |
432 | NaZhu_2023-03-12 | Geometry3k-440 | 1 | 如图所示，AB=15，AC=9，BC=12，BC⊥AC。求三角形ABC的周长。 | As shown in the diagram, AB=15, AC=9, BC=12, BC is perpendicular to AC. Find the perimeter of △ABC. | 432.png | [
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(AB),15)",
"Equal(LengthOfLine(AC),9)",
"Equal(LengthOfLine(BC),12)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(AB),15)",
"Equal(LengthOfLine(AC),9)",
"Equal(LengthOfLine(BC),12)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(PerimeterOfTriangle(ABC)) | 36 | [
"triangle_perimeter_formula(1,ABC)"
] | {"START": ["triangle_perimeter_formula(1,ABC)"]} | |
433 | NaZhu_2023-03-12 | Geometry3k-442 | 2 | 如图所示，∠AFC=70°，∠EBF=35°，AD⊥ED，EB垂直于CB。求∠FEB的大小。 | As shown in the diagram, ∠AFC=70°, ∠EBF=35°, AD is perpendicular to ED, EB⊥CB. Find the measure of ∠FEB. | 433.png | [
"Shape(DE,EF,FA,AD)",
"Shape(EB,BF,FE)",
"Shape(FB,BC,CF)",
"Shape(AF,FC)",
"Collinear(DEB)",
"Collinear(AFB)",
"Collinear(EFC)"
] | [
"Equal(MeasureOfAngle(AFC),70)",
"Equal(MeasureOfAngle(EBF),35)",
"PerpendicularBetweenLine(AD,ED)",
"PerpendicularBetweenLine(EB,CB)"
] | [
"Equal(MeasureOfAngle(AFC),70)",
"Equal(MeasureOfAngle(EBF),35)",
"PerpendicularBetweenLine(AD,ED)",
"PerpendicularBetweenLine(EB,CB)"
] | Value(MeasureOfAngle(FEB)) | 75 | [
"vertical_angle(1,AFC,BFE)",
"triangle_property_angle_sum(1,EBF)"
] | {"START": ["vertical_angle(1,AFC,BFE)", "triangle_property_angle_sum(1,EBF)"]} | |
434 | JiaZou_2023-03-12 | Geometry3k-444 | 5 | 如图所示，AD=x+2，BD=3*y-9，BD=DY，CA=AY，CB=3/2*x+11，DY=2*y+6。求x的值。 | As shown in the diagram, AD=x+2, BD=3*y-9, BD=DY, CA=AY, CB=3/2*x+11, DY=2*y+6. Find the value of x. | 434.png | [
"Shape(AY,YD,DA)",
"Shape(BC,CA,AD,DB)",
"Collinear(CAY)",
"Collinear(BDY)"
] | [
"Equal(LengthOfLine(AD),x+2)",
"Equal(LengthOfLine(BD),3*y-9)",
"Equal(LengthOfLine(BD),LengthOfLine(DY))",
"Equal(LengthOfLine(CA),LengthOfLine(AY))",
"Equal(LengthOfLine(CB),3/2*x+11)",
"Equal(LengthOfLine(DY),2*y+6)"
] | [
"Equal(LengthOfLine(AD),x+2)",
"Equal(LengthOfLine(BD),3*y-9)",
"Equal(LengthOfLine(BD),LengthOfLine(DY))",
"Equal(LengthOfLine(CA),LengthOfLine(AY))",
"Equal(LengthOfLine(CB),3/2*x+11)",
"Equal(LengthOfLine(DY),2*y+6)"
] | Value(x) | 14 | [
"line_addition(1,CA,AY)",
"line_addition(1,BD,DY)",
"similar_triangle_judgment_sas(1,YDA,YBC)",
"similar_triangle_property_line_ratio(1,AYD,CYB)",
"similar_triangle_property_line_ratio(1,YDA,YBC)"
] | {"START": ["line_addition(1,CA,AY)", "line_addition(1,BD,DY)"], "line_addition(1,BD,DY)": ["similar_triangle_judgment_sas(1,YDA,YBC)"], "line_addition(1,CA,AY)": ["similar_triangle_judgment_sas(1,YDA,YBC)"], "similar_triangle_judgment_sas(1,YDA,YBC)": ["similar_triangle_property_line_ratio(1,YDA,YBC)", "similar_triangl... | |
435 | JiaZou_2023-04-09 | Geometry3k-445 | 2 | 如图所示，AB=17，AD=6，DC=15，CD垂直于AD，DA垂直于BA，四边形DABC是梯形。求DABC的面积。 | As shown in the diagram, AB=17, AD=6, DC=15, CD⊥AD, DA⊥BA, DC and AB are the parallel sides of trapezoid DABC. Find the area of quadrilateral DABC. | 435.png | [
"Shape(DA,AB,BC,CD)"
] | [
"Equal(LengthOfLine(AB),17)",
"Equal(LengthOfLine(AD),6)",
"Equal(LengthOfLine(DC),15)",
"PerpendicularBetweenLine(CD,AD)",
"PerpendicularBetweenLine(DA,BA)",
"Trapezoid(DABC)"
] | [
"Equal(LengthOfLine(AB),17)",
"Equal(LengthOfLine(AD),6)",
"Equal(LengthOfLine(DC),15)",
"PerpendicularBetweenLine(CD,AD)",
"PerpendicularBetweenLine(DA,BA)"
] | Value(AreaOfQuadrilateral(DABC)) | 96 | [
"right_trapezoid_judgment_right_angle(1,DABC)",
"right_trapezoid_area_formular(1,DABC)"
] | {"START": ["right_trapezoid_judgment_right_angle(1,DABC)"], "right_trapezoid_judgment_right_angle(1,DABC)": ["right_trapezoid_area_formular(1,DABC)"]} | |
436 | JiaZou_2023-04-09 | Geometry3k-446 | 3 | 如图所示，BA=6，DA=9，DC=7，∠BAF=32°，∠CBF=40°，∠FAD=20°，ADCB是▱。求∠BDC的大小。 | As shown in the diagram, BA=6, DA=9, DC=7, ∠BAF=32°, ∠CBF=40°, ∠FAD=20°, quadrilateral ADCB is a ▱. Find the measure of ∠BDC. | 436.png | [
"Shape(AD,DF,FA)",
"Shape(FD,DC,CF)",
"Shape(FC,CB,BF)",
"Shape(FB,BA,AF)",
"Collinear(DFB)",
"Collinear(AFC)"
] | [
"Equal(LengthOfLine(BA),6)",
"Equal(LengthOfLine(DA),9)",
"Equal(LengthOfLine(DC),7)",
"Equal(MeasureOfAngle(BAF),32)",
"Equal(MeasureOfAngle(CBF),40)",
"Equal(MeasureOfAngle(FAD),20)",
"Parallelogram(ADCB)"
] | [
"Equal(LengthOfLine(BA),6)",
"Equal(LengthOfLine(DA),9)",
"Equal(LengthOfLine(DC),7)",
"Equal(MeasureOfAngle(BAF),32)",
"Equal(MeasureOfAngle(CBF),40)",
"Equal(MeasureOfAngle(FAD),20)"
] | Value(MeasureOfAngle(BDC)) | 88 | [
"angle_addition(1,BAF,FAD)",
"parallelogram_property_opposite_angle_equal(1,ADCB)",
"triangle_property_angle_sum(1,CBD)"
] | {"START": ["angle_addition(1,BAF,FAD)", "parallelogram_property_opposite_angle_equal(1,ADCB)", "triangle_property_angle_sum(1,CBD)"]} | |
437 | JiaZou_2023-04-09 | Geometry3k-447 | 5 | 如图所示，圆A的直径为10，圆B的直径为20，圆C的直径为14，⊙A的圆心为A，⊙B的圆心为B，圆C的圆心为C。求直线BY的长度。 | As shown in the diagram, the diameter of circle A is 10, the diameter of circle B is 20, the diameter of ⊙C is 14, the center of ⊙A is A, B is the center of circle B, C is the center of circle C. Find the length of line BY. | 437.png | [
"Shape(BEA,BAF,AEF)",
"Shape(BEA,AD,ADE)",
"Shape(DA,BAF,AFD)",
"Shape(BD,ADE,BGE,CGY,YB)",
"Shape(YB,BD,AFD,BFH,CYH)",
"Shape(YC,BCG,CGY)",
"Shape(CY,CYH,BHC)",
"Shape(BHC,BCG,CHG)",
"Collinear(ADBYC)",
"Cocircular(A,EFD)",
"Cocircular(B,HCGEAF)",
"Cocircular(C,YHG)"
] | [
"Equal(DiameterOfCircle(A),10)",
"Equal(DiameterOfCircle(B),20)",
"Equal(DiameterOfCircle(C),14)",
"IsCentreOfCircle(A,A)",
"IsCentreOfCircle(B,B)",
"IsCentreOfCircle(C,C)"
] | [
"Equal(DiameterOfCircle(A),10)",
"Equal(DiameterOfCircle(B),20)",
"Equal(DiameterOfCircle(C),14)",
"IsCentreOfCircle(A,A)",
"IsCentreOfCircle(B,B)",
"IsCentreOfCircle(C,C)"
] | Value(LengthOfLine(BY)) | 3 | [
"line_addition(1,BY,YC)",
"radius_of_circle_property_length_equal(1,BC,B)",
"radius_of_circle_property_length_equal(1,CY,C)",
"circle_property_length_of_radius_and_diameter(1,B)",
"circle_property_length_of_radius_and_diameter(1,C)"
] | {"START": ["line_addition(1,BY,YC)", "radius_of_circle_property_length_equal(1,BC,B)", "radius_of_circle_property_length_equal(1,CY,C)", "circle_property_length_of_radius_and_diameter(1,B)", "circle_property_length_of_radius_and_diameter(1,C)"]} | |
438 | JiaZou_2023-04-09 | Geometry3k-448 | 1 | 如图所示，∠EBF=26°，⌒ACD的角度为89，弧AEF的角度为x。求x的值。 | As shown in the diagram, ∠EBF=26°, the measure of ⌒ACD is 89, the measure of ⌒AEF is x. Find the value of x. | 438.png | [
"Shape(FC,ACD,DE,AEF)",
"Shape(CF,AFC)",
"Shape(ED,ADE)",
"Shape(EB,BF,AEF)",
"Collinear(CFB)",
"Collinear(DEB)",
"Cocircular(A,CDEF)"
] | [
"Equal(MeasureOfAngle(EBF),26)",
"Equal(MeasureOfArc(ACD),89)",
"Equal(MeasureOfArc(AEF),x)"
] | [
"Equal(MeasureOfAngle(EBF),26)",
"Equal(MeasureOfArc(ACD),89)",
"Equal(MeasureOfArc(AEF),x)"
] | Value(x) | 37 | [
"circle_property_circular_power_segment_and_segment_angle(2,BFC,BED,A)"
] | {"START": ["circle_property_circular_power_segment_and_segment_angle(2,BFC,BED,A)"]} | |
439 | JiaZou_2023-04-09 | Geometry3k-449 | 1 | 如图所示，AB=4*x-17，CD=2*x-1，∠BCD=4*y-19°，∠CBA=3*y+3°，CA和DB是▱ACDB的一组对边。求x的值。 | As shown in the diagram, AB=4*x-17, CD=2*x-1, ∠BCD=4*y-19°, ∠CBA=3*y+3°, CA and DB are opposite sides of the ▱ ACDB. Find the value of x. | 439.png | [
"Shape(AC,CB,BA)",
"Shape(BC,CD,DB)"
] | [
"Equal(LengthOfLine(AB),4*x-17)",
"Equal(LengthOfLine(CD),2*x-1)",
"Equal(MeasureOfAngle(BCD),4*y-19)",
"Equal(MeasureOfAngle(CBA),3*y+3)",
"Parallelogram(ACDB)"
] | [
"Equal(LengthOfLine(AB),4*x-17)",
"Equal(LengthOfLine(CD),2*x-1)",
"Equal(MeasureOfAngle(BCD),4*y-19)",
"Equal(MeasureOfAngle(CBA),3*y+3)"
] | Value(x) | 8 | [
"parallelogram_property_opposite_line_equal(1,CDBA)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,CDBA)"]} | |
440 | JiaZou_2023-03-12 | Geometry3k-450 | 1 | 如图所示，AB=9，AC=x，∠ACB=58°，∠CBA=35°。求x的值。 | As shown in the diagram, AB=9, AC=x, ∠ACB=58°, ∠CBA=35°. Find the value of x. | 440.png | [
"Shape(AC,CB,BA)"
] | [
"Equal(LengthOfLine(AB),9)",
"Equal(LengthOfLine(AC),x)",
"Equal(MeasureOfAngle(ACB),58)",
"Equal(MeasureOfAngle(CBA),35)"
] | [
"Equal(LengthOfLine(AB),9)",
"Equal(LengthOfLine(AC),x)",
"Equal(MeasureOfAngle(ACB),58)",
"Equal(MeasureOfAngle(CBA),35)"
] | Value(x) | 9*sin(7*pi/36)/sin(29*pi/90) | [
"sine_theorem(1,ACB)"
] | {"START": ["sine_theorem(1,ACB)"]} | |
441 | JiaZou_2023-04-09 | Geometry3k-451 | 3 | 如图所示，AB=3，AB=CN，AC=BN，∠ANB=62°，AC⊥NC，NB垂直于AB。求四边形ACNB的周长。 | As shown in the diagram, AB=3, AB=CN, AC=BN, ∠ANB=62°, AC is perpendicular to NC, NB is perpendicular to AB. Find the perimeter of ACNB. | 441.png | [
"Shape(AC,CN,NA)",
"Shape(AN,NB,BA)"
] | [
"Equal(LengthOfLine(AB),3)",
"Equal(LengthOfLine(AB),LengthOfLine(CN))",
"Equal(LengthOfLine(AC),LengthOfLine(BN))",
"Equal(MeasureOfAngle(ANB),62)",
"PerpendicularBetweenLine(AC,NC)",
"PerpendicularBetweenLine(NB,AB)"
] | [
"Equal(LengthOfLine(AB),3)",
"Equal(LengthOfLine(AB),LengthOfLine(CN))",
"Equal(LengthOfLine(AC),LengthOfLine(BN))",
"Equal(MeasureOfAngle(ANB),62)",
"PerpendicularBetweenLine(AC,NC)",
"PerpendicularBetweenLine(NB,AB)"
] | Value(PerimeterOfQuadrilateral(ACNB)) | 6*tan(7*pi/45)+6 | [
"triangle_property_angle_sum(1,ANB)",
"sine_theorem(1,BAN)",
"quadrilateral_perimeter_formula(1,ACNB)"
] | {"START": ["triangle_property_angle_sum(1,ANB)", "sine_theorem(1,BAN)", "quadrilateral_perimeter_formula(1,ACNB)"]} | |
442 | JiaZou_2023-04-09 | Geometry3k-452 | 1 | 如图所示，∠HMJ=79°，∠KML=77°。求∠JMK的大小。 | As shown in the diagram, ∠HMJ=79°, ∠KML=77°. Find the measure of ∠JMK. | 442.png | [
"Shape(HM,MJ,MJH)",
"Shape(LM,MH,MHL)",
"Shape(KM,ML,MLK)",
"Shape(JM,MK,MKJ)",
"Collinear(HMK)",
"Collinear(LMJ)",
"Cocircular(M,HLKJ)"
] | [
"Equal(MeasureOfAngle(HMJ),79)",
"Equal(MeasureOfAngle(KML),77)"
] | [
"Equal(MeasureOfAngle(HMJ),79)",
"Equal(MeasureOfAngle(KML),77)"
] | Value(MeasureOfAngle(JMK)) | 103 | [
"adjacent_complementary_angle(1,JMK,KML)"
] | {"START": ["adjacent_complementary_angle(1,JMK,KML)"]} | |
443 | JiaZou_2023-04-09 | Geometry3k-453 | 2 | 如图所示，∠ACD=x°，∠BCA=130°，∠DCB=60°。求x的值。 | As shown in the diagram, ∠ACD=x°, ∠BCA=130°, ∠DCB=60°. Find the value of x. | 443.png | [
"Shape(DC,CB,CBD)",
"Shape(AC,CD,CDA)",
"Shape(BC,CA,CAB)",
"Cocircular(C,DAB)"
] | [
"Equal(MeasureOfAngle(ACD),x)",
"Equal(MeasureOfAngle(BCA),130)",
"Equal(MeasureOfAngle(DCB),60)"
] | [
"Equal(MeasureOfAngle(ACD),x)",
"Equal(MeasureOfAngle(BCA),130)",
"Equal(MeasureOfAngle(DCB),60)"
] | Value(x) | 170 | [
"angle_addition(1,DCB,BCA)",
"round_angle(1,DCA,ACD)"
] | {"START": ["angle_addition(1,DCB,BCA)", "round_angle(1,DCA,ACD)"]} | |
444 | JiaZou_2023-04-09 | Geometry3k-454 | 6 | 如图所示，∠MPG=89°，弧PNE的角度为66，P是圆P的圆心。求∠MNG的大小。 | As shown in the diagram, ∠MPG=89°, the measure of arc PNE is 66, the center of circle P is P. Find the measure of ∠MNG. | 444.png | [
"Shape(GE,PEG)",
"Shape(MG,PGM)",
"Shape(NM,PMN)",
"Shape(EN,PNE)",
"Shape(GP,PB,BE,EG)",
"Shape(GM,MP,PG)",
"Shape(PM,MB,BP)",
"Shape(BM,MN,NB)",
"Shape(BN,NE,EB)",
"Collinear(GPBN)",
"Collinear(MBE)",
"Cocircular(P,GMNE)"
] | [
"Equal(MeasureOfAngle(MPG),89)",
"Equal(MeasureOfArc(PNE),66)",
"IsCentreOfCircle(P,P)"
] | [
"Equal(MeasureOfAngle(MPG),89)",
"Equal(MeasureOfArc(PNE),66)",
"IsCentreOfCircle(P,P)"
] | Value(MeasureOfAngle(MNG)) | 89/2 | [
"adjacent_complementary_angle(1,NPM,MPG)",
"triangle_property_angle_sum(1,PMN)",
"radius_of_circle_property_length_equal(1,PM,P)",
"radius_of_circle_property_length_equal(1,PN,P)",
"isosceles_triangle_judgment_line_equal(1,PMN)",
"isosceles_triangle_property_angle_equal(1,PMN)"
] | {"START": ["adjacent_complementary_angle(1,NPM,MPG)", "triangle_property_angle_sum(1,PMN)", "radius_of_circle_property_length_equal(1,PM,P)", "radius_of_circle_property_length_equal(1,PN,P)"], "isosceles_triangle_judgment_line_equal(1,PMN)": ["isosceles_triangle_property_angle_equal(1,PMN)"], "radius_of_circle_property... | |
445 | JiaZou_2023-03-12 | Geometry3k-455 | 2 | 如图所示，AB=18，AC=9，BC=x，BC垂直于AC。求x的值。 | As shown in the diagram, AB=18, AC=9, BC=x, BC is perpendicular to AC. Find the value of x. | 445.png | [
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(AB),18)",
"Equal(LengthOfLine(AC),9)",
"Equal(LengthOfLine(BC),x)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(AB),18)",
"Equal(LengthOfLine(AC),9)",
"Equal(LengthOfLine(BC),x)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(x) | 9*sqrt(3) | [
"right_triangle_judgment_angle(1,BCA)",
"right_triangle_property_pythagorean(1,BCA)"
] | {"START": ["right_triangle_judgment_angle(1,BCA)"], "right_triangle_judgment_angle(1,BCA)": ["right_triangle_property_pythagorean(1,BCA)"]} | |
446 | JiaZou_2023-04-09 | Geometry3k-456 | 3 | 如图所示，BDAC的面积为177，AD=11，AE=13，BC=x，AE⊥BE，BDAC是梯形。求x的值。 | As shown in the diagram, the area of quadrilateral BDAC is 177, AD=11, AE=13, BC=x, AE⊥BE, BC and DA are the parallel sides of trapezoid BDAC. Find the value of x. | 446.png | [
"Shape(BD,DA,AE,EB)",
"Shape(EA,AC,CE)",
"Collinear(BEC)"
] | [
"Equal(AreaOfQuadrilateral(BDAC),177)",
"Equal(LengthOfLine(AD),11)",
"Equal(LengthOfLine(AE),13)",
"Equal(LengthOfLine(BC),x)",
"PerpendicularBetweenLine(AE,BE)",
"Trapezoid(BDAC)"
] | [
"Equal(AreaOfQuadrilateral(BDAC),177)",
"Equal(LengthOfLine(AD),11)",
"Equal(LengthOfLine(AE),13)",
"Equal(LengthOfLine(BC),x)",
"PerpendicularBetweenLine(AE,BE)",
"Trapezoid(BDAC)"
] | Value(x) | 211/13 | [
"adjacent_complementary_angle(1,CEA,AEB)",
"altitude_of_quadrilateral_judgment_left_vertex(2,AE,ACBD)",
"trapezoid_area_formula(1,ACBD)"
] | {"START": ["adjacent_complementary_angle(1,CEA,AEB)", "trapezoid_area_formula(1,ACBD)"], "adjacent_complementary_angle(1,CEA,AEB)": ["altitude_of_quadrilateral_judgment_left_vertex(2,AE,ACBD)"]} | |
447 | JiaZou_2023-03-12 | Geometry3k-457 | 1 | 如图所示，AB=18，AD=y，BC=x，BD=z，∠ABC=45°，∠ADB=60°，BA⊥DA，BC⊥AC。求z的值。 | As shown in the diagram, AB=18, AD=y, BC=x, BD=z, ∠ABC=45°, ∠ADB=60°, BA is perpendicular to DA, BC is perpendicular to AC. Find the value of z. | 447.png | [
"Shape(BA,AD,DB)",
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(AB),18)",
"Equal(LengthOfLine(AD),y)",
"Equal(LengthOfLine(BC),x)",
"Equal(LengthOfLine(BD),z)",
"Equal(MeasureOfAngle(ABC),45)",
"Equal(MeasureOfAngle(ADB),60)",
"PerpendicularBetweenLine(BA,DA)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(AB),18)",
"Equal(LengthOfLine(AD),y)",
"Equal(LengthOfLine(BC),x)",
"Equal(LengthOfLine(BD),z)",
"Equal(MeasureOfAngle(ABC),45)",
"Equal(MeasureOfAngle(ADB),60)",
"PerpendicularBetweenLine(BA,DA)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(z) | 12*sqrt(3) | [
"sine_theorem(1,BAD)"
] | {"START": ["sine_theorem(1,BAD)"]} | |
448 | JiaZou_2023-04-09 | Geometry3k-458 | 1 | 如图所示，RP=y+4，RS=27，TP=2*y-5，TQ=5*x，∠PQT=95°，∠RQP=33°，∠TSP=3*z°，QR和TS是平行四边形QTSR的一组对边。求y的值。 | As shown in the diagram, RP=y+4, RS=27, TP=2*y-5, TQ=5*x, ∠PQT=95°, ∠RQP=33°, ∠TSP=3*z°, QR and TS are opposite sides of the ▱ QTSR. Find the value of y. | 448.png | [
"Shape(QT,TP,PQ)",
"Shape(PT,TS,SP)",
"Shape(PS,SR,RP)",
"Shape(PR,RQ,QP)",
"Collinear(QPS)",
"Collinear(TPR)"
] | [
"Equal(LengthOfLine(RP),y+4)",
"Equal(LengthOfLine(RS),27)",
"Equal(LengthOfLine(TP),2*y-5)",
"Equal(LengthOfLine(TQ),5*x)",
"Equal(MeasureOfAngle(PQT),95)",
"Equal(MeasureOfAngle(RQP),33)",
"Equal(MeasureOfAngle(TSP),3*z)",
"Parallelogram(QTSR)"
] | [
"Equal(LengthOfLine(RP),y+4)",
"Equal(LengthOfLine(RS),27)",
"Equal(LengthOfLine(TP),2*y-5)",
"Equal(LengthOfLine(TQ),5*x)",
"Equal(MeasureOfAngle(PQT),95)",
"Equal(MeasureOfAngle(RQP),33)",
"Equal(MeasureOfAngle(TSP),3*z)",
"Parallelogram(QTSR)"
] | Value(y) | 9 | [
"parallelogram_property_diagonal_bisection(1,TSRQ,P)"
] | {"START": ["parallelogram_property_diagonal_bisection(1,TSRQ,P)"]} | |
449 | JiaZou_2023-03-12 | Geometry3k-459 | 7 | 如图所示，AB=6，AC=4，DC=2，CD⊥AD，CD垂直于BD。求△CBA的周长。 | As shown in the diagram, AB=6, AC=4, DC=2, CD is perpendicular to AD, CD⊥BD. Find the perimeter of triangle CBA. | 449.png | [
"Shape(CB,BD,DC)",
"Shape(CD,DA,AC)",
"Collinear(BDA)"
] | [
"Equal(LengthOfLine(AB),6)",
"Equal(LengthOfLine(AC),4)",
"Equal(LengthOfLine(DC),2)",
"PerpendicularBetweenLine(CD,AD)",
"PerpendicularBetweenLine(CD,BD)"
] | [
"Equal(LengthOfLine(AB),6)",
"Equal(LengthOfLine(AC),4)",
"Equal(LengthOfLine(DC),2)",
"PerpendicularBetweenLine(CD,AD)",
"PerpendicularBetweenLine(CD,BD)"
] | Value(PerimeterOfTriangle(CBA)) | 2*sqrt(13-6*sqrt(3))+10 | [
"adjacent_complementary_angle(1,BDC,CDA)",
"right_triangle_judgment_angle(1,BDC)",
"right_triangle_judgment_angle(1,CDA)",
"line_addition(1,BD,DA)",
"right_triangle_property_pythagorean(1,BDC)",
"right_triangle_property_pythagorean(1,CDA)",
"triangle_perimeter_formula(1,BAC)"
] | {"START": ["adjacent_complementary_angle(1,BDC,CDA)", "right_triangle_judgment_angle(1,CDA)", "line_addition(1,BD,DA)", "triangle_perimeter_formula(1,BAC)"], "adjacent_complementary_angle(1,BDC,CDA)": ["right_triangle_judgment_angle(1,BDC)"], "right_triangle_judgment_angle(1,BDC)": ["right_triangle_property_pythagorean... | |
450 | JiaZou_2023-04-09 | Geometry3k-460 | 0 | 如图所示，∠BCD=2*x-20°，∠CDE=x°，∠DEA=2*x+10°，AB⊥CB，EA⊥BA。求∠ABC的大小。 | As shown in the diagram, ∠BCD=2*x-20°, ∠CDE=x°, ∠DEA=2*x+10°, AB is perpendicular to CB, EA⊥BA. Find the measure of ∠ABC. | 450.png | [
"Shape(AB,BC,CD,DE,EA)"
] | [
"Equal(MeasureOfAngle(BCD),2*x-20)",
"Equal(MeasureOfAngle(CDE),x)",
"Equal(MeasureOfAngle(DEA),2*x+10)",
"PerpendicularBetweenLine(AB,CB)",
"PerpendicularBetweenLine(EA,BA)"
] | [
"Equal(MeasureOfAngle(BCD),2*x-20)",
"Equal(MeasureOfAngle(CDE),x)",
"Equal(MeasureOfAngle(DEA),2*x+10)",
"PerpendicularBetweenLine(AB,CB)",
"PerpendicularBetweenLine(EA,BA)"
] | Value(MeasureOfAngle(ABC)) | 90 | [] | {"START": []} | |
451 | JiaZou_2023-03-12 | Geometry3k-461 | 1 | 如图所示，AB=10，AC=x，BC=y，∠CBA=45°，AC⊥BC。求x的值。 | As shown in the diagram, AB=10, AC=x, BC=y, ∠CBA=45°, AC is perpendicular to BC. Find the value of x. | 451.png | [
"Shape(AC,CB,BA)"
] | [
"Equal(LengthOfLine(AB),10)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),y)",
"Equal(MeasureOfAngle(CBA),45)",
"PerpendicularBetweenLine(AC,BC)"
] | [
"Equal(LengthOfLine(AB),10)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),y)",
"Equal(MeasureOfAngle(CBA),45)",
"PerpendicularBetweenLine(AC,BC)"
] | Value(x) | 5*sqrt(2) | [
"sine_theorem(1,ACB)"
] | {"START": ["sine_theorem(1,ACB)"]} | |
452 | JiaZou_2023-04-09 | Geometry3k-462 | 1 | 如图所示，∠CFD=x+36°，∠DEC=2*y°，∠ECF=78°，∠FDE=110°，CE平行于FD。求x的值。 | As shown in the diagram, ∠CFD=x+36°, ∠DEC=2*y°, ∠ECF=78°, ∠FDE=110°, CE is parallel to FD. Find the value of x. | 452.png | [
"Shape(EC,CF,FD,DE)"
] | [
"Equal(MeasureOfAngle(CFD),x+36)",
"Equal(MeasureOfAngle(DEC),2*y)",
"Equal(MeasureOfAngle(ECF),78)",
"Equal(MeasureOfAngle(FDE),110)",
"ParallelBetweenLine(CE,FD)"
] | [
"Equal(MeasureOfAngle(CFD),x+36)",
"Equal(MeasureOfAngle(DEC),2*y)",
"Equal(MeasureOfAngle(ECF),78)",
"Equal(MeasureOfAngle(FDE),110)",
"ParallelBetweenLine(CE,FD)"
] | Value(x) | 66 | [
"parallel_property_ipsilateral_internal_angle(1,CE,FD)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,CE,FD)"]} | |
453 | JiaZou_2023-03-12 | Geometry3k-463 | 1 | 如图所示，AB=6，AC=6*sqrt(2)，BC=6，∠BCA=x°。求x的值。 | As shown in the diagram, AB=6, AC=6*sqrt(2), BC=6, ∠BCA=x°. Find the value of x. | 453.png | [
"Shape(BC,CA,AB)"
] | [
"Equal(LengthOfLine(AB),6)",
"Equal(LengthOfLine(AC),6*sqrt(2))",
"Equal(LengthOfLine(BC),6)",
"Equal(MeasureOfAngle(BCA),x)"
] | [
"Equal(LengthOfLine(AB),6)",
"Equal(LengthOfLine(AC),6*sqrt(2))",
"Equal(LengthOfLine(BC),6)",
"Equal(MeasureOfAngle(BCA),x)"
] | Value(x) | 45 | [
"cosine_theorem(1,CAB)"
] | {"START": ["cosine_theorem(1,CAB)"]} | |
454 | YimingHe_2023-04-02 | Geometry3k-464 | 2 | 如图所示，∠GFH=130°，HF垂直于JF。求∠JFG的大小。 | As shown in the diagram, ∠GFH=130°, HF⊥JF. Find the measure of ∠JFG. | 454.png | [
"Shape(FG,FGJ,JF)",
"Shape(FJ,FJH,HF)",
"Shape(FH,FHG,GF)",
"Cocircular(F,GJH)"
] | [
"Equal(MeasureOfAngle(GFH),130)",
"PerpendicularBetweenLine(HF,JF)"
] | [
"Equal(MeasureOfAngle(GFH),130)",
"PerpendicularBetweenLine(HF,JF)"
] | Value(MeasureOfAngle(JFG)) | 140 | [
"angle_addition(1,GFH,HFJ)",
"round_angle(1,GFJ,JFG)"
] | {"START": ["angle_addition(1,GFH,HFJ)", "round_angle(1,GFJ,JFG)"]} | |
455 | YimingHe_2023-04-02 | Geometry3k-465 | 2 | 如图所示，AE=x，BE=2/3*x，CE=4*y，DE=3*y+4，四边形CABD是▱。求y的值。 | As shown in the diagram, AE=x, BE=2/3*x, CE=4*y, DE=3*y+4, AC and BD are opposite sides of the ▱ CABD. Find the value of y. | 455.png | [
"Shape(CA,AE,EC)",
"Shape(EA,AB,BE)",
"Shape(EB,BD,DE)",
"Shape(ED,DC,CE)",
"Collinear(AED)",
"Collinear(CEB)"
] | [
"Equal(LengthOfLine(AE),x)",
"Equal(LengthOfLine(BE),2/3*x)",
"Equal(LengthOfLine(CE),4*y)",
"Equal(LengthOfLine(DE),3*y+4)",
"Parallelogram(CABD)"
] | [
"Equal(LengthOfLine(AE),x)",
"Equal(LengthOfLine(BE),2/3*x)",
"Equal(LengthOfLine(CE),4*y)",
"Equal(LengthOfLine(DE),3*y+4)",
"Parallelogram(CABD)"
] | Value(y) | 4/3 | [
"parallelogram_property_diagonal_bisection(1,CABD,E)",
"parallelogram_property_diagonal_bisection(1,ABDC,E)"
] | {"START": ["parallelogram_property_diagonal_bisection(1,CABD,E)", "parallelogram_property_diagonal_bisection(1,ABDC,E)"]} | |
456 | YimingHe_2023-04-02 | Geometry3k-466 | 3 | 如图所示，AE=4，BE=3，DA和DC是风筝形BADC的一组临边。求直线AB的长度。 | As shown in the diagram, AE=4, BE=3, DA and DC are one pair of adjacent sides of the kite BADC. Find the length of line AB. | 456.png | [
"Shape(AD,DE,EA)",
"Shape(DC,CE,ED)",
"Shape(AE,EB,BA)",
"Shape(EC,CB,BE)",
"Collinear(AEC)",
"Collinear(DEB)"
] | [
"Equal(LengthOfLine(AE),4)",
"Equal(LengthOfLine(BE),3)",
"Kite(BADC)"
] | [
"Equal(LengthOfLine(AE),4)",
"Equal(LengthOfLine(BE),3)",
"Kite(BADC)"
] | Value(LengthOfLine(AB)) | 5 | [
"kite_property_diagonal_perpendicular_bisection(1,BADC,E)",
"right_triangle_judgment_angle(1,AEB)",
"right_triangle_property_pythagorean(1,AEB)"
] | {"START": ["kite_property_diagonal_perpendicular_bisection(1,BADC,E)"], "kite_property_diagonal_perpendicular_bisection(1,BADC,E)": ["right_triangle_judgment_angle(1,AEB)"], "right_triangle_judgment_angle(1,AEB)": ["right_triangle_property_pythagorean(1,AEB)"]} | |
457 | JiaZou_2023-03-12 | Geometry3k-467 | 2 | 如图所示，AB=y，AC=5，BC=x，∠BAC=60°，AC⊥BC。求y的值。 | As shown in the diagram, AB=y, AC=5, BC=x, ∠BAC=60°, AC⊥BC. Find the value of y. | 457.png | [
"Shape(AC,CB,BA)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),5)",
"Equal(LengthOfLine(BC),x)",
"Equal(MeasureOfAngle(BAC),60)",
"PerpendicularBetweenLine(AC,BC)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),5)",
"Equal(LengthOfLine(BC),x)",
"Equal(MeasureOfAngle(BAC),60)",
"PerpendicularBetweenLine(AC,BC)"
] | Value(y) | 10 | [
"triangle_property_angle_sum(1,ACB)",
"sine_theorem(1,ACB)"
] | {"START": ["triangle_property_angle_sum(1,ACB)", "sine_theorem(1,ACB)"]} | |
458 | YimingHe_2023-04-02 | Geometry3k-468 | 3 | 如图所示，∠AGE=55°，∠BGA=x°，∠GBH=y°，BD平行于GA。求y的值。 | As shown in the diagram, ∠AGE=55°, ∠BGA=x°, ∠GBH=y°, BD∥GA. Find the value of y. | 458.png | [
"Shape(HB,BF)",
"Shape(CG,GB)",
"Shape(GB,BH)",
"Shape(EG,GC)",
"Shape(AG,GE)",
"Shape(DB,BG)",
"Shape(BG,GA)",
"Shape(FB,BD)",
"Collinear(HBD)",
"Collinear(CGA)",
"Collinear(FBGE)"
] | [
"Equal(MeasureOfAngle(AGE),55)",
"Equal(MeasureOfAngle(BGA),x)",
"Equal(MeasureOfAngle(GBH),y)",
"ParallelBetweenLine(BD,GA)"
] | [
"Equal(MeasureOfAngle(AGE),55)",
"Equal(MeasureOfAngle(BGA),x)",
"Equal(MeasureOfAngle(GBH),y)",
"ParallelBetweenLine(BD,GA)"
] | Value(y) | 125 | [
"parallel_property_ipsilateral_internal_angle(1,BD,GA)",
"adjacent_complementary_angle(1,BGA,AGE)",
"adjacent_complementary_angle(1,DBG,GBH)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,BD,GA)", "adjacent_complementary_angle(1,BGA,AGE)", "adjacent_complementary_angle(1,DBG,GBH)"]} | |
459 | YimingHe_2023-04-02 | Geometry3k-469 | 1 | 如图所示，∠LCR=3*x+5°，∠MCN=60°，∠RCM=x-1°。求∠LCR的大小。 | As shown in the diagram, ∠LCR=3*x+5°, ∠MCN=60°, ∠RCM=x-1°. Find the measure of ∠LCR. | 459.png | [
"Shape(CR,CRL,LC)",
"Shape(CM,CMR,RC)",
"Shape(CN,CNM,MC)",
"Shape(CL,CLN,NC)",
"Collinear(LCM)",
"Cocircular(C,LNMR)"
] | [
"Equal(MeasureOfAngle(LCR),3*x+5)",
"Equal(MeasureOfAngle(MCN),60)",
"Equal(MeasureOfAngle(RCM),x-1)"
] | [
"Equal(MeasureOfAngle(LCR),3*x+5)",
"Equal(MeasureOfAngle(MCN),60)",
"Equal(MeasureOfAngle(RCM),x-1)"
] | Value(MeasureOfAngle(LCR)) | 137 | [
"adjacent_complementary_angle(1,LCR,RCM)"
] | {"START": ["adjacent_complementary_angle(1,LCR,RCM)"]} | |
460 | YimingHe_2023-04-02 | Geometry3k-470 | 6 | 如图所示，CE=7，ED=x，⊙C的圆心为C，DB是⊙O的切线，CE垂直于DE，DB⊥CB，ED⊥BD。求x的值。 | As shown in the diagram, CE=7, ED=x, the center of circle C is C, DB is the tangent to ⊙C, CE is perpendicular to DE, DB⊥CB, ED⊥BD. Find the value of x. | 460.png | [
"Shape(ED,DB,CEB)",
"Shape(CE,CEB,BC)",
"Shape(CB,CBE,EC)",
"Cocircular(C,BE)"
] | [
"Equal(LengthOfLine(CE),7)",
"Equal(LengthOfLine(ED),x)",
"IsCentreOfCircle(C,C)",
"IsTangentOfCircle(DB,C,B)",
"PerpendicularBetweenLine(CE,DE)",
"PerpendicularBetweenLine(DB,CB)",
"PerpendicularBetweenLine(ED,BD)"
] | [
"Equal(LengthOfLine(CE),7)",
"Equal(LengthOfLine(ED),x)",
"IsCentreOfCircle(C,C)",
"IsTangentOfCircle(DB,C,B)",
"PerpendicularBetweenLine(CE,DE)",
"PerpendicularBetweenLine(DB,CB)",
"PerpendicularBetweenLine(ED,BD)"
] | Value(x) | 7 | [
"parallel_judgment_ipsilateral_internal_angle(1,DE,BC)",
"parallel_judgment_ipsilateral_internal_angle(1,EC,DB)",
"parallelogram_judgment_parallel_and_parallel(1,EDBC)",
"parallelogram_property_opposite_line_equal(1,EDBC)",
"radius_of_circle_property_length_equal(1,CE,C)",
"radius_of_circle_property_lengt... | {"START": ["parallel_judgment_ipsilateral_internal_angle(1,DE,BC)", "parallel_judgment_ipsilateral_internal_angle(1,EC,DB)", "radius_of_circle_property_length_equal(1,CE,C)", "radius_of_circle_property_length_equal(1,CB,C)"], "parallel_judgment_ipsilateral_internal_angle(1,DE,BC)": ["parallelogram_judgment_parallel_and... | |
461 | YimingHe_2023-04-02 | Geometry3k-471 | 1 | 如图所示，四边形BCAD的高为14，AC=8，DB=4，EF⊥FF，四边形BCAD是梯形。求四边形BCAD的面积。 | As shown in the diagram, the height of quadrilateral BCAD is 14, AC=8, DB=4, EF is perpendicular to FF, BD and CA are the parallel sides of trapezoid BCAD. Find the area of BCAD. | 461.png | [
"Shape(BC,CA,AD,DB)"
] | [
"Equal(HeightOfQuadrilateral(BCAD),14)",
"Equal(LengthOfLine(AC),8)",
"Equal(LengthOfLine(DB),4)",
"PerpendicularBetweenLine(EF,FA)",
"Trapezoid(BCAD)"
] | [
"Equal(HeightOfQuadrilateral(BCAD),14)",
"Equal(LengthOfLine(AC),8)",
"Equal(LengthOfLine(DB),4)",
"PerpendicularBetweenLine(EF,FA)",
"Trapezoid(BCAD)"
] | Value(AreaOfQuadrilateral(BCAD)) | 84 | [
"trapezoid_area_formula(1,BCAD)"
] | {"START": ["trapezoid_area_formula(1,BCAD)"]} | |
462 | YimingHe_2023-04-02 | Geometry3k-472 | 16 | 如图所示，AB=35，CD=19，四边形DBAC的周长为74，四边形DBAC是等腰梯形，CF垂直于AF，DE垂直于AE。求DBAC的面积。 | As shown in the diagram, AB=35, CD=19, the perimeter of quadrilateral DBAC is 74, DBAC is a isosceles trapezoid, CF⊥AF, DE⊥AE. Find the area of DBAC. | 462.png | [
"Shape(DB,BE,ED)",
"Shape(DE,EF,FC,CD)",
"Shape(CF,FA,AC)",
"Collinear(BEFA)"
] | [
"Equal(LengthOfLine(AB),35)",
"Equal(LengthOfLine(CD),19)",
"Equal(PerimeterOfQuadrilateral(DBAC),74)",
"IsoscelesTrapezoid(DBAC)",
"PerpendicularBetweenLine(CF,AF)",
"PerpendicularBetweenLine(DE,AE)"
] | [
"Equal(LengthOfLine(AB),35)",
"Equal(LengthOfLine(CD),19)",
"PerpendicularBetweenLine(CF,AF)",
"PerpendicularBetweenLine(DE,AE)"
] | Value(AreaOfQuadrilateral(DBAC)) | 162 | [
"quadrilateral_perimeter_formula(1,DBAC)",
"adjacent_complementary_angle(1,BED,DEF)",
"adjacent_complementary_angle(1,BFC,CFA)",
"altitude_of_quadrilateral_judgment_left_vertex(2,DE,DBAC)",
"altitude_of_quadrilateral_judgment_right_vertex(2,CF,DBAC)",
"parallel_judgment_ipsilateral_internal_angle(1,DC,EF)... | {"START": ["quadrilateral_perimeter_formula(1,DBAC)", "adjacent_complementary_angle(1,BED,DEF)", "adjacent_complementary_angle(1,BFC,CFA)", "line_addition(1,BE,EF)", "line_addition(1,BF,FA)", "trapezoid_area_formula(1,DBAC)"], "adjacent_complementary_angle(1,BED,DEF)": ["altitude_of_quadrilateral_judgment_left_vertex(2... | |
463 | YimingHe_2023-04-02 | Geometry3k-473 | 1 | 如图所示，∠RST=63°，A是⊙A的圆心。求⌒ATR的角度。 | As shown in the diagram, ∠RST=63°, the center of ⊙A is A. Find the measure of ⌒ATR. | 463.png | [
"Shape(SR,ARS)",
"Shape(TS,AST)",
"Shape(AT,ATR,RA)",
"Shape(ST,TA,AR,RS)",
"Cocircular(A,RST)"
] | [
"Equal(MeasureOfAngle(RST),63)",
"IsCentreOfCircle(A,A)"
] | [
"Equal(MeasureOfAngle(RST),63)",
"IsCentreOfCircle(A,A)"
] | Value(MeasureOfArc(ATR)) | 126 | [
"arc_property_circumference_angle_external(1,ATR,S)"
] | {"START": ["arc_property_circumference_angle_external(1,ATR,S)"]} | |
464 | YimingHe_2023-04-02 | Geometry3k-474 | 4 | 如图所示，∠BPY=3*x°，弧PAC的角度为2*x+15，弧PCY的角度为3*x-3，P是圆P的圆心。求⌒PCY的角度。 | As shown in the diagram, ∠BPY=3*x°, the measure of arc PAC is 2*x+15, the measure of arc PCY is 3*x-3, P is the center of circle P. Find the measure of ⌒PCY. | 464.png | [
"Shape(BP,PY,PYB)",
"Shape(PC,PCY,YP)",
"Shape(PA,PAC,CP)",
"Shape(PX,PXA,AP)",
"Shape(PB,PBX,XP)",
"Collinear(BPA)",
"Cocircular(P,BXACY)"
] | [
"Equal(MeasureOfAngle(BPY),3*x)",
"Equal(MeasureOfArc(PAC),2*x+15)",
"Equal(MeasureOfArc(PCY),3*x-3)",
"IsCentreOfCircle(P,P)"
] | [
"Equal(MeasureOfAngle(BPY),3*x)",
"Equal(MeasureOfArc(PAC),2*x+15)",
"Equal(MeasureOfArc(PCY),3*x-3)",
"IsCentreOfCircle(P,P)"
] | Value(MeasureOfArc(PCY)) | 60 | [
"arc_property_center_angle(1,PCY,P)",
"arc_property_center_angle(1,PAC,P)",
"angle_addition(1,BPY,YPC)",
"adjacent_complementary_angle(1,BPC,CPA)"
] | {"START": ["arc_property_center_angle(1,PCY,P)", "arc_property_center_angle(1,PAC,P)", "angle_addition(1,BPY,YPC)", "adjacent_complementary_angle(1,BPC,CPA)"]} | |
465 | YimingHe_2023-04-02 | Geometry3k-475 | 2 | 如图所示，∠FYD=4*y+10°，EH平行于BY，YH垂直于EH。求y的值。 | As shown in the diagram, ∠FYD=4*y+10°, EH is parallel to BY, YH is perpendicular to EH. Find the value of y. | 465.png | [
"Shape(EH,HJ)",
"Shape(JH,HA)",
"Shape(YH,HE)",
"Shape(BY,YH)",
"Shape(DY,YB)",
"Shape(FY,YD)",
"Shape(HY,YF)",
"Shape(AH,HY)",
"Collinear(JHYD)",
"Collinear(EHA)",
"Collinear(BYF)"
] | [
"Equal(MeasureOfAngle(FYD),4*y+10)",
"ParallelBetweenLine(EH,BY)",
"PerpendicularBetweenLine(YH,EH)"
] | [
"Equal(MeasureOfAngle(FYD),4*y+10)"
] | Value(y) | 20 | [
"parallel_property_ipsilateral_internal_angle(1,YB,HE)",
"vertical_angle(1,BYH,FYD)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,YB,HE)", "vertical_angle(1,BYH,FYD)"]} | |
466 | YimingHe_2023-04-02 | Geometry3k-476 | 3 | 如图所示，∠CBD=12°，⌒GEB的角度为28。求∠BKE的大小。 | As shown in the diagram, ∠CBD=12°, the measure of arc GEB is 28. Find the measure of ∠BKE. | 466.png | [
"Shape(GCE,EK,KC)",
"Shape(GEB,BK,KE)",
"Shape(GBD,DB)",
"Shape(KB,BD,DK)",
"Shape(GDC,CK,KD)",
"Collinear(EKD)",
"Collinear(CKB)",
"Cocircular(G,EBDC)"
] | [
"Equal(MeasureOfAngle(CBD),12)",
"Equal(MeasureOfArc(GEB),28)"
] | [
"Equal(MeasureOfAngle(CBD),12)",
"Equal(MeasureOfArc(GEB),28)"
] | Value(MeasureOfAngle(BKE)) | 26 | [
"arc_property_circumference_angle_external(1,GEB,D)",
"triangle_property_angle_sum(1,KBD)",
"adjacent_complementary_angle(1,DKB,BKE)"
] | {"START": ["arc_property_circumference_angle_external(1,GEB,D)", "triangle_property_angle_sum(1,KBD)", "adjacent_complementary_angle(1,DKB,BKE)"]} | |
467 | JiaZou_2023-03-12 | Geometry3k-477 | 1 | 如图所示，BC=32，BC=AB，BD=y，CD=x，∠CAB=54°，BD⊥AD，CD垂直于BD。求y的值。 | As shown in the diagram, BC=32, BC=AB, BD=y, CD=x, ∠CAB=54°, BD⊥AD, CD is perpendicular to BD. Find the value of y. | 467.png | [
"Shape(BC,CD,DB)",
"Shape(BD,DA,AB)",
"Collinear(CDA)"
] | [
"Equal(LengthOfLine(BC),32)",
"Equal(LengthOfLine(BC),LengthOfLine(AB))",
"Equal(LengthOfLine(BD),y)",
"Equal(LengthOfLine(CD),x)",
"Equal(MeasureOfAngle(CAB),54)",
"PerpendicularBetweenLine(BD,AD)",
"PerpendicularBetweenLine(CD,BD)"
] | [
"Equal(LengthOfLine(BC),32)",
"Equal(LengthOfLine(BC),LengthOfLine(AB))",
"Equal(LengthOfLine(BD),y)",
"Equal(LengthOfLine(CD),x)",
"Equal(MeasureOfAngle(CAB),54)",
"PerpendicularBetweenLine(BD,AD)",
"PerpendicularBetweenLine(CD,BD)"
] | Value(y) | 8+8*sqrt(5) | [
"sine_theorem(1,BDA)"
] | {"START": ["sine_theorem(1,BDA)"]} | |
468 | YimingHe_2023-04-02 | Geometry3k-478 | 6 | 如图所示，DE=7，EX=24，D是圆D的圆心，DA垂直于XA，XE垂直于DE。求直线AX的长度。 | As shown in the diagram, DE=7, EX=24, the center of ⊙D is D, DA is perpendicular to XA, XE is perpendicular to DE. Find the length of line AX. | 468.png | [
"Shape(AX,XQ,DAQ)",
"Shape(DAQ,QD,DA)",
"Shape(DT,DTA,AD)",
"Shape(QX,XE,DQE)",
"Shape(DQ,DQE,ED)",
"Shape(DE,DET,TD)",
"Collinear(XQDT)",
"Cocircular(D,AQET)"
] | [
"Equal(LengthOfLine(DE),7)",
"Equal(LengthOfLine(EX),24)",
"IsCentreOfCircle(D,D)",
"PerpendicularBetweenLine(DA,XA)",
"PerpendicularBetweenLine(XE,DE)"
] | [
"IsCentreOfCircle(D,D)",
"PerpendicularBetweenLine(DA,XA)",
"PerpendicularBetweenLine(XE,DE)"
] | Value(LengthOfLine(AX)) | 24 | [
"radius_of_circle_property_length_equal(1,DA,D)",
"radius_of_circle_property_length_equal(1,DE,D)",
"right_triangle_judgment_angle(1,XED)",
"right_triangle_judgment_angle(1,DAX)",
"right_triangle_property_pythagorean(1,DAX)",
"right_triangle_property_pythagorean(1,XED)"
] | {"START": ["radius_of_circle_property_length_equal(1,DA,D)", "radius_of_circle_property_length_equal(1,DE,D)", "right_triangle_judgment_angle(1,XED)", "right_triangle_judgment_angle(1,DAX)"], "right_triangle_judgment_angle(1,DAX)": ["right_triangle_property_pythagorean(1,DAX)"], "right_triangle_judgment_angle(1,XED)": ... | |
469 | YimingHe_2023-04-02 | Geometry3k-479 | 3 | 如图所示，∠CBI=84°，∠HBD=x°，∠IBH=16°，DB⊥CB。求x的值。 | As shown in the diagram, ∠CBI=84°, ∠HBD=x°, ∠IBH=16°, DB is perpendicular to CB. Find the value of x. | 469.png | [
"Shape(BC,BCD,DB)",
"Shape(BD,BDH,HB)",
"Shape(BH,BHI,IB)",
"Shape(BI,BIC,CB)",
"Cocircular(B,DHIC)"
] | [
"Equal(MeasureOfAngle(CBI),84)",
"Equal(MeasureOfAngle(HBD),x)",
"Equal(MeasureOfAngle(IBH),16)",
"PerpendicularBetweenLine(DB,CB)"
] | [
"Equal(MeasureOfAngle(CBI),84)",
"Equal(MeasureOfAngle(HBD),x)",
"Equal(MeasureOfAngle(IBH),16)",
"PerpendicularBetweenLine(DB,CB)"
] | Value(x) | 170 | [
"angle_addition(1,DBC,CBI)",
"angle_addition(1,IBH,HBD)",
"round_angle(1,DBI,IBD)"
] | {"START": ["angle_addition(1,DBC,CBI)", "angle_addition(1,IBH,HBD)", "round_angle(1,DBI,IBD)"]} | |
470 | YimingHe_2023-04-02 | Geometry3k-481 | 2 | 如图所示，∠AQT=32°，∠QSR=5*x+4°，∠QTR=6*x-2°。求∠SRT的大小。 | As shown in the diagram, ∠AQT=32°, ∠QSR=5*x+4°, ∠QTR=6*x-2°. Find the measure of ∠SRT. | 470.png | [
"Shape(CSR,RS)",
"Shape(AS,SR,RA)",
"Shape(AR,CRQ,QA)",
"Shape(AQ,QT,TA)",
"Shape(CQT,TQ)",
"Shape(AT,CTS,SA)",
"Collinear(RAT)",
"Collinear(QAS)",
"Cocircular(C,RQTS)"
] | [
"Equal(MeasureOfAngle(AQT),32)",
"Equal(MeasureOfAngle(QSR),5*x+4)",
"Equal(MeasureOfAngle(QTR),6*x-2)"
] | [
"Equal(MeasureOfAngle(AQT),32)",
"Equal(MeasureOfAngle(QSR),5*x+4)",
"Equal(MeasureOfAngle(QTR),6*x-2)"
] | Value(MeasureOfAngle(SRT)) | 32 | [
"arc_property_circumference_angle_external(1,CTS,R)",
"arc_property_circumference_angle_external(1,CTS,Q)"
] | {"START": ["arc_property_circumference_angle_external(1,CTS,R)", "arc_property_circumference_angle_external(1,CTS,Q)"]} | |
471 | YimingHe_2023-04-02 | Geometry3k-482 | 3 | 如图所示，WZ=4，XW=3，XZ=b，XW⊥ZW，XWZY是矩形。求直线YW的长度。 | As shown in the diagram, WZ=4, XW=3, XZ=b, XW is perpendicular to ZW, quadrilateral XWZY is a rectangle. Find the length of line YW. | 471.png | [
"Shape(AY,YX,XA)",
"Shape(AX,XW,WA)",
"Shape(AW,WZ,ZA)",
"Shape(AZ,ZY,YA)",
"Collinear(XAZ)",
"Collinear(WAY)"
] | [
"Equal(LengthOfLine(WZ),4)",
"Equal(LengthOfLine(XW),3)",
"Equal(LengthOfLine(XZ),b)",
"PerpendicularBetweenLine(XW,ZW)",
"Rectangle(XWZY)"
] | [
"PerpendicularBetweenLine(XW,ZW)"
] | Value(LengthOfLine(YW)) | 5 | [
"right_triangle_judgment_angle(1,XWZ)",
"right_triangle_property_pythagorean(1,XWZ)",
"rectangle_property_diagonal_equal(1,XWZY)"
] | {"START": ["right_triangle_judgment_angle(1,XWZ)", "rectangle_property_diagonal_equal(1,XWZY)"], "right_triangle_judgment_angle(1,XWZ)": ["right_triangle_property_pythagorean(1,XWZ)"]} | |
472 | YimingHe_2023-04-02 | Geometry3k-483 | 1 | 如图所示，AB=5*y，DC=y+8，∠CDA=4*x°，∠DAB=2*x-6°，四边形DABC是平行四边形。求y的值。 | As shown in the diagram, AB=5*y, DC=y+8, ∠CDA=4*x°, ∠DAB=2*x-6°, quadrilateral DABC is a parallelogram. Find the value of y. | 472.png | [
"Shape(DA,AB,BC,CD)"
] | [
"Equal(LengthOfLine(AB),5*y)",
"Equal(LengthOfLine(DC),y+8)",
"Equal(MeasureOfAngle(CDA),4*x)",
"Equal(MeasureOfAngle(DAB),2*x-6)",
"Parallelogram(DABC)"
] | [
"Equal(LengthOfLine(AB),5*y)",
"Equal(LengthOfLine(DC),y+8)",
"Equal(MeasureOfAngle(CDA),4*x)",
"Equal(MeasureOfAngle(DAB),2*x-6)",
"Parallelogram(DABC)"
] | Value(y) | 2 | [
"parallelogram_property_opposite_line_equal(1,CDAB)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,CDAB)"]} | |
473 | YimingHe_2023-04-02 | Geometry3k-484 | 6 | 如图所示，BE=16，BF=x，CF=12，DE=16，C是⊙C的圆心，BE是⊙O的切线，DE是⊙O的切线。求x的值。 | As shown in the diagram, BE=16, BF=x, CF=12, DE=16, C is the center of circle C, the tangent to ⊙C is BE, DE is the tangent to circle C. Find the value of x. | 473.png | [
"Shape(BE,CFE,FB)",
"Shape(FC,CA,CAF)",
"Shape(CEA,ED,DA)",
"Shape(CF,CFE,EC)",
"Shape(CE,CEA,AC)",
"Collinear(BFC)",
"Collinear(CAD)",
"Collinear(BED)",
"Cocircular(C,FEA)"
] | [
"Equal(LengthOfLine(BE),16)",
"Equal(LengthOfLine(BF),x)",
"Equal(LengthOfLine(CF),12)",
"Equal(LengthOfLine(DE),16)",
"IsCentreOfCircle(C,C)",
"IsTangentOfCircle(BE,C)",
"IsTangentOfCircle(DE,C)"
] | [
"Equal(LengthOfLine(BE),16)",
"Equal(LengthOfLine(BF),x)",
"Equal(LengthOfLine(CF),12)",
"Equal(LengthOfLine(DE),16)",
"IsCentreOfCircle(C,C)"
] | Value(x) | 8 | [
"tangent_of_circle_property_perpendicular(2,BE,C,C)",
"radius_of_circle_property_length_equal(1,CF,C)",
"radius_of_circle_property_length_equal(1,CE,C)",
"line_addition(1,CF,FB)",
"right_triangle_judgment_angle(1,BEC)",
"right_triangle_property_pythagorean(1,BEC)"
] | {"START": ["tangent_of_circle_property_perpendicular(2,BE,C,C)", "radius_of_circle_property_length_equal(1,CF,C)", "radius_of_circle_property_length_equal(1,CE,C)", "line_addition(1,CF,FB)"], "right_triangle_judgment_angle(1,BEC)": ["right_triangle_property_pythagorean(1,BEC)"], "tangent_of_circle_property_perpendicula... | |
474 | YimingHe_2023-04-02 | Geometry3k-485 | 3 | 如图所示，BG=7，DC=14，⊙B的圆心为B，四边形ADCE是正方形。求ADCE的面积减去⊙B的面积。 | As shown in the diagram, BG=7, DC=14, the center of ⊙B is B, quadrilateral ADCE is a square. Find the area of ADCE minus the area of the circle B. | 474.png | [
"Shape(AF,BIF,IA)",
"Shape(FD,DG,BFG)",
"Shape(GC,CH,BGH)",
"Shape(HE,EI,BHI)",
"Shape(BIF,BFG,BGH,BHI)",
"Shape(BG)",
"Collinear(AFD)",
"Collinear(DGC)",
"Collinear(CHE)",
"Collinear(AIE)",
"Cocircular(B,FGHI)"
] | [
"Equal(LengthOfLine(BG),7)",
"Equal(LengthOfLine(DC),14)",
"IsCentreOfCircle(B,B)",
"Square(ADCE)"
] | [
"Equal(LengthOfLine(BG),7)",
"Equal(LengthOfLine(DC),14)",
"IsCentreOfCircle(B,B)"
] | Value(Sub(AreaOfQuadrilateral(ADCE),AreaOfCircle(B))) | 196-49*pi | [
"parallelogram_area_formula_sine(1,ADCE)",
"radius_of_circle_property_length_equal(1,BG,B)",
"circle_area_formula(1,B)"
] | {"START": ["parallelogram_area_formula_sine(1,ADCE)", "radius_of_circle_property_length_equal(1,BG,B)", "circle_area_formula(1,B)"]} | |
475 | YimingHe_2023-04-02 | Geometry3k-486 | 1 | 如图所示，∠BCD=2*x+4°，∠ECB=2*x-4°。求∠ECB的大小。 | As shown in the diagram, ∠BCD=2*x+4°, ∠ECB=2*x-4°. Find the measure of ∠ECB. | 475.png | [
"Shape(EC,CB)",
"Shape(BC,CD)",
"Shape(DC,CA)",
"Shape(AC,CE)",
"Collinear(BCA)",
"Collinear(ECD)"
] | [
"Equal(MeasureOfAngle(BCD),2*x+4)",
"Equal(MeasureOfAngle(ECB),2*x-4)"
] | [
"Equal(MeasureOfAngle(BCD),2*x+4)",
"Equal(MeasureOfAngle(ECB),2*x-4)"
] | Value(MeasureOfAngle(ECB)) | 86 | [
"adjacent_complementary_angle(1,ECB,BCD)"
] | {"START": ["adjacent_complementary_angle(1,ECB,BCD)"]} | |
476 | YimingHe_2023-04-02 | Geometry3k-487 | 2 | 如图所示，TQ=3*x-8，TS=x+10，圆O的切线为TQ，⊙O的切线为TR，TR是⊙O的切线，圆O的切线为TS。求x的值。 | As shown in the diagram, TQ=3*x-8, TS=x+10, the tangent to ⊙A is TQ, the tangent to ⊙A is TR, TR is the tangent to circle B, TS is the tangent to circle B. Find the value of x. | 476.png | [
"Shape(QT,TR,AQR)",
"Shape(AQR,ARQ)",
"Shape(RT,TS,BRS)",
"Shape(BRS,BSR)",
"Cocircular(A,QR)",
"Cocircular(B,RS)"
] | [
"Equal(LengthOfLine(TQ),3*x-8)",
"Equal(LengthOfLine(TS),x+10)",
"IsTangentOfCircle(TQ,A)",
"IsTangentOfCircle(TR,A)",
"IsTangentOfCircle(TR,B)",
"IsTangentOfCircle(TS,B)"
] | [
"Equal(LengthOfLine(TQ),3*x-8)",
"Equal(LengthOfLine(TS),x+10)"
] | Value(x) | 9 | [
"tangent_of_circle_property_length_equal(1,TQ,TR,A)",
"tangent_of_circle_property_length_equal(1,TR,TS,B)"
] | {"START": ["tangent_of_circle_property_length_equal(1,TQ,TR,A)", "tangent_of_circle_property_length_equal(1,TR,TS,B)"]} | |
477 | YimingHe_2023-04-02 | Geometry3k-488 | 8 | 如图所示，PR=3，⊙P的半径为5，P是⊙P的圆心，PR⊥QR。求直线QS的长度。 | As shown in the diagram, PR=3, the radius of ⊙P is 5, P is the center of circle P, PR is perpendicular to QR. Find the length of line QS. | 477.png | [
"Shape(PQ,PQS,SP)",
"Shape(PR,RQ,QP)",
"Shape(PS,SR,RP)",
"Shape(PSQ,QS)",
"Collinear(QRS)",
"Cocircular(P,SQ)"
] | [
"Equal(LengthOfLine(PR),3)",
"Equal(RadiusOfCircle(P),5)",
"IsCentreOfCircle(P,P)",
"PerpendicularBetweenLine(PR,QR)"
] | [
"IsCentreOfCircle(P,P)",
"PerpendicularBetweenLine(PR,QR)"
] | Value(LengthOfLine(QS)) | 8 | [
"radius_of_circle_property_length_equal(1,PQ,P)",
"radius_of_circle_property_length_equal(1,PS,P)",
"adjacent_complementary_angle(1,SRP,PRQ)",
"right_triangle_judgment_angle(1,PRQ)",
"right_triangle_property_pythagorean(1,PRQ)",
"right_triangle_judgment_angle(1,SRP)",
"right_triangle_property_pythagorea... | {"START": ["radius_of_circle_property_length_equal(1,PQ,P)", "radius_of_circle_property_length_equal(1,PS,P)", "adjacent_complementary_angle(1,SRP,PRQ)", "right_triangle_judgment_angle(1,PRQ)", "line_addition(1,QR,RS)"], "adjacent_complementary_angle(1,SRP,PRQ)": ["right_triangle_judgment_angle(1,SRP)"], "right_triangl... | |
478 | YimingHe_2023-04-02 | Geometry3k-489 | 2 | 如图所示，CB=18，CE=13，ED=24，CE是CEDB的高，CE垂直于DE，CE和DB是梯形CEDB的腰。求四边形CEDB的面积。 | As shown in the diagram, CB=18, CE=13, ED=24, the height of quadrilateral CEDB is CE, CE is perpendicular to DE, CB and ED are the parallel sides of trapezoid CEDB. Find the area of quadrilateral CEDB. | 478.png | [
"Shape(CE,ED,DB,BC)"
] | [
"Equal(LengthOfLine(CB),18)",
"Equal(LengthOfLine(CE),13)",
"Equal(LengthOfLine(ED),24)",
"IsAltitudeOfQuadrilateral(CE,CEDB)",
"PerpendicularBetweenLine(CE,DE)",
"Trapezoid(CEDB)"
] | [
"Equal(LengthOfLine(CB),18)",
"Equal(LengthOfLine(CE),13)",
"Equal(LengthOfLine(ED),24)",
"IsAltitudeOfQuadrilateral(CE,CEDB)",
"PerpendicularBetweenLine(CE,DE)"
] | Value(AreaOfQuadrilateral(CEDB)) | 273 | [
"right_trapezoid_judgment_right_angle(1,CEDB)",
"right_trapezoid_area_formular(1,CEDB)"
] | {"START": ["right_trapezoid_judgment_right_angle(1,CEDB)"], "right_trapezoid_judgment_right_angle(1,CEDB)": ["right_trapezoid_area_formular(1,CEDB)"]} | |
479 | YimingHe_2023-04-02 | Geometry3k-490 | 1 | 如图所示，AB=96-y，AD=5*x-18，BC=2*x，DC=3*y，CBAD是平行四边形。求y的值。 | As shown in the diagram, AB=96-y, AD=5*x-18, BC=2*x, DC=3*y, CBAD is a parallelogram. Find the value of y. | 479.png | [
"Shape(CB,BA,AD,DC)"
] | [
"Equal(LengthOfLine(AB),96-y)",
"Equal(LengthOfLine(AD),5*x-18)",
"Equal(LengthOfLine(BC),2*x)",
"Equal(LengthOfLine(DC),3*y)",
"Parallelogram(CBAD)"
] | [
"Equal(LengthOfLine(AB),96-y)",
"Equal(LengthOfLine(AD),5*x-18)",
"Equal(LengthOfLine(BC),2*x)",
"Equal(LengthOfLine(DC),3*y)",
"Parallelogram(CBAD)"
] | Value(y) | 24 | [
"parallelogram_property_opposite_line_equal(1,DCBA)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,DCBA)"]} | |
480 | JiaZou_2023-03-12 | Geometry3k-491 | 1 | 如图所示，AF=24，AH=25，BH=11，∠ABH=30°，∠GCH=28°，△ABC的内心为H，BG垂直于HG，HD垂直于BD，HF⊥AF。求直线DH的长度。 | As shown in the diagram, AF=24, AH=25, BH=11, ∠ABH=30°, ∠GCH=28°, the incenter of triangle ABC is H, BG⊥HG, HD is perpendicular to BD, HF⊥AF. Find the length of line DH. | 480.png | [
"Shape(AD,DH,HA)",
"Shape(DB,BH,HD)",
"Shape(BG,GH,HB)",
"Shape(GC,CH,HG)",
"Shape(CF,FH,HC)",
"Shape(HF,FA,AH)",
"Collinear(ADB)",
"Collinear(AFC)",
"Collinear(BGC)"
] | [
"Equal(LengthOfLine(AF),24)",
"Equal(LengthOfLine(AH),25)",
"Equal(LengthOfLine(BH),11)",
"Equal(MeasureOfAngle(ABH),30)",
"Equal(MeasureOfAngle(GCH),28)",
"IsIncenterOfTriangle(H,ABC)",
"PerpendicularBetweenLine(BG,HG)",
"PerpendicularBetweenLine(HD,BD)",
"PerpendicularBetweenLine(HF,AF)"
] | [
"Equal(LengthOfLine(AF),24)",
"Equal(LengthOfLine(AH),25)",
"Equal(LengthOfLine(BH),11)",
"Equal(MeasureOfAngle(ABH),30)",
"Equal(MeasureOfAngle(GCH),28)",
"PerpendicularBetweenLine(BG,HG)",
"PerpendicularBetweenLine(HD,BD)",
"PerpendicularBetweenLine(HF,AF)"
] | Value(LengthOfLine(DH)) | 11/2 | [
"sine_theorem(1,HDB)"
] | {"START": ["sine_theorem(1,HDB)"]} | |
481 | YimingHe_2023-04-02 | Geometry3k-492 | 3 | 如图所示，AB=15，PB=12，∠DBA=24°，四边形ADCB是菱形。求直线CP的长度。 | As shown in the diagram, AB=15, PB=12, ∠DBA=24°, quadrilateral ADCB is a rhombus. Find the length of line CP. | 481.png | [
"Shape(AD,DP,PA)",
"Shape(PD,DC,CP)",
"Shape(PC,CB,BP)",
"Shape(PB,BA,AP)",
"Collinear(APC)",
"Collinear(DPB)"
] | [
"Equal(LengthOfLine(AB),15)",
"Equal(LengthOfLine(PB),12)",
"Equal(MeasureOfAngle(DBA),24)",
"Rhombus(ADCB)"
] | [
"Equal(LengthOfLine(AB),15)",
"Equal(LengthOfLine(PB),12)",
"Equal(MeasureOfAngle(DBA),24)",
"Rhombus(ADCB)"
] | Value(LengthOfLine(CP)) | 9 | [
"kite_property_diagonal_perpendicular_bisection(1,BADC,P)",
"right_triangle_judgment_angle(1,APB)",
"right_triangle_property_pythagorean(1,APB)"
] | {"START": ["kite_property_diagonal_perpendicular_bisection(1,BADC,P)"], "kite_property_diagonal_perpendicular_bisection(1,BADC,P)": ["right_triangle_judgment_angle(1,APB)"], "right_triangle_judgment_angle(1,APB)": ["right_triangle_property_pythagorean(1,APB)"]} | |
482 | JiaZou_2023-03-12 | Geometry3k-493 | 4 | 如图所示，∠DBA=17°，∠DEA=29°，AD⊥BD。求∠AEB的大小。 | As shown in the diagram, ∠DBA=17°, ∠DEA=29°, AD⊥BD. Find the measure of ∠AEB. | 482.png | [
"Shape(AD,DE,EA)",
"Shape(AE,EB,BA)",
"Collinear(DEB)"
] | [
"Equal(MeasureOfAngle(DBA),17)",
"Equal(MeasureOfAngle(DEA),29)",
"PerpendicularBetweenLine(AD,BD)"
] | [
"Equal(MeasureOfAngle(DBA),17)",
"Equal(MeasureOfAngle(DEA),29)",
"PerpendicularBetweenLine(AD,BD)"
] | Value(MeasureOfAngle(AEB)) | 151 | [
"angle_addition(1,BAE,EAD)",
"triangle_property_angle_sum(1,ADE)",
"triangle_property_angle_sum(1,AEB)",
"triangle_property_angle_sum(1,DBA)"
] | {"START": ["angle_addition(1,BAE,EAD)", "triangle_property_angle_sum(1,ADE)", "triangle_property_angle_sum(1,AEB)", "triangle_property_angle_sum(1,DBA)"]} | |
483 | YimingHe_2023-04-02 | Geometry3k-494 | 1 | 如图所示，∠FEI=2*x+70°，∠HGL=2*y-20°，∠RFN=3*x+40°，FN平行于EI，GF平行于HE。求x的值。 | As shown in the diagram, ∠FEI=2*x+70°, ∠HGL=2*y-20°, ∠RFN=3*x+40°, FN∥EI, GF is parallel to HE. Find the value of x. | 483.png | [
"Shape(LG,GQ)",
"Shape(HG,GL)",
"Shape(PH,HG)",
"Shape(MH,HP)",
"Shape(EH,HM)",
"Shape(QG,GF)",
"Shape(OE,EH)",
"Shape(GF,FR)",
"Shape(HE,EF,FG,GH)",
"Shape(RF,FN)",
"Shape(NF,FE)",
"Shape(FE,EI)",
"Shape(IE,EO)",
"Collinear(QGHM)",
"Collinear(RFEO)",
"Collinear(LGFN)",
"Collinear(PH... | [
"Equal(MeasureOfAngle(FEI),2*x+70)",
"Equal(MeasureOfAngle(HGL),2*y-20)",
"Equal(MeasureOfAngle(RFN),3*x+40)",
"ParallelBetweenLine(FN,EI)",
"ParallelBetweenLine(GF,HE)"
] | [
"ParallelBetweenLine(FN,EI)",
"ParallelBetweenLine(GF,HE)"
] | Value(x) | 30 | [
"parallel_property_corresponding_angle(1,FN,EI,R)"
] | {"START": ["parallel_property_corresponding_angle(1,FN,EI,R)"]} | |
484 | JiaZou_2023-03-12 | Geometry3k-495 | 1 | 如图所示，AB=5*x+5，AC=4*x，BC=8*x+9，△ABC的周长为65。求直线AC的长度。 | As shown in the diagram, AB=5*x+5, AC=4*x, BC=8*x+9, the perimeter of triangle ABC is 65. Find the length of line AC. | 484.png | [
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(AB),5*x+5)",
"Equal(LengthOfLine(AC),4*x)",
"Equal(LengthOfLine(BC),8*x+9)",
"Equal(PerimeterOfTriangle(ABC),65)"
] | [
"Equal(LengthOfLine(AB),5*x+5)",
"Equal(LengthOfLine(AC),4*x)",
"Equal(LengthOfLine(BC),8*x+9)",
"Equal(PerimeterOfTriangle(ABC),65)"
] | Value(LengthOfLine(AC)) | 12 | [
"triangle_perimeter_formula(1,ABC)"
] | {"START": ["triangle_perimeter_formula(1,ABC)"]} | |
485 | YimingHe_2023-04-02 | Geometry3k-496 | 1 | 如图所示，∠NMQ=10*x°，∠PNM=20*x°，∠PNM=∠MQP，∠QPN=∠NMQ，四边形MQPN是平行四边形。求∠QPN的大小。 | As shown in the diagram, ∠NMQ=10*x°, ∠PNM=20*x°, ∠PNM=∠MQP, ∠QPN=∠NMQ, quadrilateral MQPN is a ▱. Find the measure of ∠QPN. | 485.png | [
"Shape(MQ,QP,PN,NM)"
] | [
"Equal(MeasureOfAngle(NMQ),10*x)",
"Equal(MeasureOfAngle(PNM),20*x)",
"Equal(MeasureOfAngle(PNM),MeasureOfAngle(MQP))",
"Equal(MeasureOfAngle(QPN),MeasureOfAngle(NMQ))",
"Parallelogram(MQPN)"
] | [
"Equal(MeasureOfAngle(NMQ),10*x)",
"Equal(MeasureOfAngle(PNM),20*x)",
"Equal(MeasureOfAngle(PNM),MeasureOfAngle(MQP))",
"Equal(MeasureOfAngle(QPN),MeasureOfAngle(NMQ))",
"Parallelogram(MQPN)"
] | Value(MeasureOfAngle(QPN)) | 60 | [
"parallel_property_ipsilateral_internal_angle(1,NP,MQ)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,NP,MQ)"]} | |
486 | YimingHe_2023-04-02 | Geometry3k-497 | 1 | 如图所示，BTAC的面积为153，AT=9，BD是四边形BTAC的高，BTAC是平行四边形，BD垂直于TD。求直线BD的长度。 | As shown in the diagram, the area of quadrilateral BTAC is 153, AT=9, the height of quadrilateral BTAC is BD, BTAC is a parallelogram, BD⊥TD. Find the length of line BD. | 486.png | [
"Shape(BD,DT,TB)",
"Shape(BT,TA,AC,CB)",
"Collinear(DTA)"
] | [
"Equal(AreaOfQuadrilateral(BTAC),153)",
"Equal(LengthOfLine(AT),9)",
"IsAltitudeOfQuadrilateral(BD,BTAC)",
"Parallelogram(BTAC)",
"PerpendicularBetweenLine(BD,TD)"
] | [
"Equal(LengthOfLine(AT),9)",
"IsAltitudeOfQuadrilateral(BD,BTAC)",
"Parallelogram(BTAC)",
"PerpendicularBetweenLine(BD,TD)"
] | Value(LengthOfLine(BD)) | 17 | [
"parallelogram_area_formula_common(1,BTAC)"
] | {"START": ["parallelogram_area_formula_common(1,BTAC)"]} | |
487 | YimingHe_2023-04-02 | Geometry3k-498 | 3 | 如图所示，DC=3，∠EDC=57°，D是圆D的圆心。求扇形DCE的面积。 | As shown in the diagram, DC=3, ∠EDC=57°, the center of ⊙D is D. Find the area of the sector DCE. | 487.png | [
"Shape(DC,DCE,ED)",
"Shape(DE,DEC,CD)",
"Cocircular(D,CE)"
] | [
"Equal(LengthOfLine(DC),3)",
"Equal(MeasureOfAngle(EDC),57)",
"IsCentreOfCircle(D,D)"
] | [
"Equal(LengthOfLine(DC),3)",
"Equal(MeasureOfAngle(EDC),57)",
"IsCentreOfCircle(D,D)"
] | Value(AreaOfSector(DCE)) | 57*pi/40 | [
"sector_area_formula(1,DCE)",
"arc_property_center_angle(1,DCE,D)",
"radius_of_circle_property_length_equal(1,DC,D)"
] | {"START": ["sector_area_formula(1,DCE)", "arc_property_center_angle(1,DCE,D)", "radius_of_circle_property_length_equal(1,DC,D)"]} | |
488 | YimingHe_2023-04-02 | Geometry3k-499 | 1 | 如图所示，MO=6*x+14，PN=9*x+5，MNOP是矩形。求x的值。 | As shown in the diagram, MO=6*x+14, PN=9*x+5, MNOP is a rectangle. Find the value of x. | 488.png | [
"Shape(AP,PM,MA)",
"Shape(AO,OP,PA)",
"Shape(AN,NO,OA)",
"Shape(AM,MN,NA)",
"Collinear(PAN)",
"Collinear(MAO)"
] | [
"Equal(LengthOfLine(MO),6*x+14)",
"Equal(LengthOfLine(PN),9*x+5)",
"Rectangle(MNOP)"
] | [] | Value(x) | 3 | [
"rectangle_property_diagonal_equal(1,MNOP)"
] | {"START": ["rectangle_property_diagonal_equal(1,MNOP)"]} | |
489 | YimingHe_2023-04-02 | Geometry3k-500 | 2 | 如图所示，∠ADC=x°，∠BAD=3*x°，CB⊥AB，DC垂直于BC。求∠ADC的大小。 | As shown in the diagram, ∠ADC=x°, ∠BAD=3*x°, CB is perpendicular to AB, DC⊥BC. Find the measure of ∠ADC. | 489.png | [
"Shape(AD,DC,CB,BA)"
] | [
"Equal(MeasureOfAngle(ADC),x)",
"Equal(MeasureOfAngle(BAD),3*x)",
"PerpendicularBetweenLine(CB,AB)",
"PerpendicularBetweenLine(DC,BC)"
] | [
"Equal(MeasureOfAngle(ADC),x)",
"Equal(MeasureOfAngle(BAD),3*x)",
"PerpendicularBetweenLine(CB,AB)",
"PerpendicularBetweenLine(DC,BC)"
] | Value(MeasureOfAngle(ADC)) | 45 | [
"parallel_judgment_ipsilateral_internal_angle(1,CD,BA)",
"parallel_property_ipsilateral_internal_angle(1,AB,DC)"
] | {"START": ["parallel_judgment_ipsilateral_internal_angle(1,CD,BA)"], "parallel_judgment_ipsilateral_internal_angle(1,CD,BA)": ["parallel_property_ipsilateral_internal_angle(1,AB,DC)"]} | |
490 | YimingHe_2023-04-02 | Geometry3k-501 | 1 | 如图所示，∠FJE=75°。求∠CJF的大小。 | As shown in the diagram, ∠FJE=75°. Find the measure of ∠CJF. | 490.png | [
"Shape(CJ,JF)",
"Shape(FJ,JE)",
"Collinear(CJE)"
] | [
"Equal(MeasureOfAngle(FJE),75)"
] | [
"Equal(MeasureOfAngle(FJE),75)"
] | Value(MeasureOfAngle(CJF)) | 105 | [
"adjacent_complementary_angle(1,CJF,FJE)"
] | {"START": ["adjacent_complementary_angle(1,CJF,FJE)"]} | |
491 | YimingHe_2023-04-02 | Geometry3k-502 | 6 | 如图所示，∠JKL=62°，⊙A的圆心为A。求⌒AJK的角度。 | As shown in the diagram, ∠JKL=62°, A is the center of circle A. Find the measure of ⌒AJK. | 491.png | [
"Shape(AL,ALJ,JA)",
"Shape(AJ,JK,KA)",
"Shape(AJK,KJ)",
"Shape(AK,AKL,LA)",
"Collinear(LAK)",
"Cocircular(A,LJK)"
] | [
"Equal(MeasureOfAngle(JKL),62)",
"IsCentreOfCircle(A,A)"
] | [
"Equal(MeasureOfAngle(JKL),62)",
"IsCentreOfCircle(A,A)"
] | Value(MeasureOfArc(AJK)) | 56 | [
"radius_of_circle_property_length_equal(1,AJ,A)",
"radius_of_circle_property_length_equal(1,AK,A)",
"isosceles_triangle_judgment_line_equal(1,AJK)",
"isosceles_triangle_property_angle_equal(1,AJK)",
"triangle_property_angle_sum(1,AJK)",
"arc_property_center_angle(1,AJK,A)"
] | {"START": ["radius_of_circle_property_length_equal(1,AJ,A)", "radius_of_circle_property_length_equal(1,AK,A)", "triangle_property_angle_sum(1,AJK)", "arc_property_center_angle(1,AJK,A)"], "isosceles_triangle_judgment_line_equal(1,AJK)": ["isosceles_triangle_property_angle_equal(1,AJK)"], "radius_of_circle_property_leng... | |
492 | JiaZou_2023-03-12 | Geometry3k-503 | 4 | 如图所示，AC=y，AD=8，BC=z，BD=25/2，CD=x，BC⊥AC，CD垂直于BD。求z的值。 | As shown in the diagram, AC=y, AD=8, BC=z, BD=25/2, CD=x, BC⊥AC, CD⊥BD. Find the value of z. | 492.png | [
"Shape(CA,AD,DC)",
"Shape(CD,DB,BC)",
"Collinear(ADB)"
] | [
"Equal(LengthOfLine(AC),y)",
"Equal(LengthOfLine(AD),8)",
"Equal(LengthOfLine(BC),z)",
"Equal(LengthOfLine(BD),25/2)",
"Equal(LengthOfLine(CD),x)",
"PerpendicularBetweenLine(BC,AC)",
"PerpendicularBetweenLine(CD,BD)"
] | [
"Equal(LengthOfLine(AC),y)",
"Equal(LengthOfLine(AD),8)",
"Equal(LengthOfLine(BC),z)",
"Equal(LengthOfLine(BD),25/2)",
"Equal(LengthOfLine(CD),x)",
"PerpendicularBetweenLine(BC,AC)",
"PerpendicularBetweenLine(CD,BD)"
] | Value(z) | 5*sqrt(41)/2 | [
"mirror_similar_triangle_judgment_aa(1,CDB,ABC)",
"line_addition(1,AD,DB)",
"mirror_similar_triangle_property_line_ratio(1,CDB,ABC)",
"mirror_similar_triangle_property_line_ratio(1,DBC,CAB)"
] | {"START": ["mirror_similar_triangle_judgment_aa(1,CDB,ABC)", "line_addition(1,AD,DB)"], "mirror_similar_triangle_judgment_aa(1,CDB,ABC)": ["mirror_similar_triangle_property_line_ratio(1,CDB,ABC)", "mirror_similar_triangle_property_line_ratio(1,DBC,CAB)"]} | |
493 | JiaZou_2023-03-12 | Geometry3k-504 | 1 | 如图所示，∠RTS=47°，SU⊥TU，TS⊥RS，TV垂直于UV。求∠VUT的大小。 | As shown in the diagram, ∠RTS=47°, SU is perpendicular to TU, TS is perpendicular to RS, TV⊥UV. Find the measure of ∠VUT. | 493.png | [
"Shape(SR,RU,US)",
"Shape(SU,UV,VS)",
"Shape(VU,UT,TV)",
"Collinear(RUT)",
"Collinear(SVT)"
] | [
"Equal(MeasureOfAngle(RTS),47)",
"PerpendicularBetweenLine(SU,TU)",
"PerpendicularBetweenLine(TS,RS)",
"PerpendicularBetweenLine(TV,UV)"
] | [
"Equal(MeasureOfAngle(RTS),47)",
"PerpendicularBetweenLine(SU,TU)",
"PerpendicularBetweenLine(TS,RS)",
"PerpendicularBetweenLine(TV,UV)"
] | Value(MeasureOfAngle(VUT)) | 43 | [
"triangle_property_angle_sum(1,VUT)"
] | {"START": ["triangle_property_angle_sum(1,VUT)"]} | |
494 | YimingHe_2023-04-02 | Geometry3k-505 | 2 | 如图所示，∠AHD=14*x+9°，∠FEG=5*x+90°，HD∥EB。求x的值。 | As shown in the diagram, ∠AHD=14*x+9°, ∠FEG=5*x+90°, HD∥EB. Find the value of x. | 494.png | [
"Shape(CH,HA)",
"Shape(AH,HD)",
"Shape(EH,HC)",
"Shape(DH,HE)",
"Shape(GE,EH)",
"Shape(HE,EB)",
"Shape(FE,EG)",
"Shape(BE,EF)",
"Collinear(CHD)",
"Collinear(GEB)",
"Collinear(AHEF)"
] | [
"Equal(MeasureOfAngle(AHD),14*x+9)",
"Equal(MeasureOfAngle(FEG),5*x+90)",
"ParallelBetweenLine(HD,EB)"
] | [
"Equal(MeasureOfAngle(AHD),14*x+9)",
"Equal(MeasureOfAngle(FEG),5*x+90)",
"ParallelBetweenLine(HD,EB)"
] | Value(x) | 9 | [
"parallel_property_corresponding_angle(1,HD,EB,A)",
"vertical_angle(1,HEB,FEG)"
] | {"START": ["parallel_property_corresponding_angle(1,HD,EB,A)", "vertical_angle(1,HEB,FEG)"]} | |
495 | YimingHe_2023-04-02 | Geometry3k-506 | 3 | 如图所示，AD=24，⊙N的圆心为N，圆N的直径为AD。求直线CN的长度。 | As shown in the diagram, AD=24, the center of ⊙N is N, the diameter of ⊙N is AD. Find the length of line CN. | 495.png | [
"Shape(AN,NB,NBA)",
"Shape(NC,CB,BN)",
"Shape(NCB,BC)",
"Shape(ND,NDC,CN)",
"Shape(NA,NAE,ED,DN)",
"Shape(NED,DE)",
"Collinear(AND)",
"Cocircular(N,AEDCB)"
] | [
"Equal(LengthOfLine(AD),24)",
"IsCentreOfCircle(N,N)",
"IsDiameterOfCircle(AD,N)"
] | [
"IsCentreOfCircle(N,N)",
"IsDiameterOfCircle(AD,N)"
] | Value(LengthOfLine(CN)) | 12 | [
"diameter_of_circle_property_length_equal(1,AD,N)",
"circle_property_length_of_radius_and_diameter(1,N)",
"radius_of_circle_property_length_equal(1,NC,N)"
] | {"START": ["diameter_of_circle_property_length_equal(1,AD,N)", "circle_property_length_of_radius_and_diameter(1,N)", "radius_of_circle_property_length_equal(1,NC,N)"]} | |
496 | YimingHe_2023-04-02 | Geometry3k-507 | 0 | 如图所示，BF=2*y+4，DG=3/2*x+8，DG=FG，EB=3*y-6，FG=1/2*x+12。求x的值。 | As shown in the diagram, BF=2*y+4, DG=3/2*x+8, DG=FG, EB=3*y-6, FG=1/2*x+12. Find the value of x. | 496.png | [
"Shape(FG,GB,BF)",
"Shape(BG,FD,DE,EB)",
"Collinear(FGD)",
"Collinear(FBE)"
] | [
"Equal(LengthOfLine(BF),2*y+4)",
"Equal(LengthOfLine(DG),3/2*x+8)",
"Equal(LengthOfLine(DG),LengthOfLine(FG))",
"Equal(LengthOfLine(EB),3*y-6)",
"Equal(LengthOfLine(FG),1/2*x+12)"
] | [
"Equal(LengthOfLine(BF),2*y+4)",
"Equal(LengthOfLine(DG),3/2*x+8)",
"Equal(LengthOfLine(DG),LengthOfLine(FG))",
"Equal(LengthOfLine(EB),3*y-6)",
"Equal(LengthOfLine(FG),1/2*x+12)"
] | Value(x) | 4 | [] | {"START": []} | |
497 | YimingHe_2023-04-02 | Geometry3k-508 | 2 | 如图所示，∠TWV=3*x-4°，∠UTW=x°，∠VUT=3*x-4°，∠WVU=x°。求∠VUT的大小。 | As shown in the diagram, ∠TWV=3*x-4°, ∠UTW=x°, ∠VUT=3*x-4°, ∠WVU=x°. Find the measure of ∠VUT. | 497.png | [
"Shape(UT,TW,WV,VU)"
] | [
"Equal(MeasureOfAngle(TWV),3*x-4)",
"Equal(MeasureOfAngle(UTW),x)",
"Equal(MeasureOfAngle(VUT),3*x-4)",
"Equal(MeasureOfAngle(WVU),x)"
] | [
"Equal(MeasureOfAngle(TWV),3*x-4)",
"Equal(MeasureOfAngle(UTW),x)",
"Equal(MeasureOfAngle(VUT),3*x-4)",
"Equal(MeasureOfAngle(WVU),x)"
] | Value(MeasureOfAngle(VUT)) | 134 | [
"parallelogram_judgment_angle_and_angle(1,UTWV)",
"parallel_property_ipsilateral_internal_angle(1,UV,TW)"
] | {"START": ["parallelogram_judgment_angle_and_angle(1,UTWV)"], "parallelogram_judgment_angle_and_angle(1,UTWV)": ["parallel_property_ipsilateral_internal_angle(1,UV,TW)"]} | |
498 | JiaZou_2023-03-12 | Geometry3k-509 | 3 | 如图所示，LJ=KL，∠JKL=70°。求∠KLJ的大小。 | As shown in the diagram, LJ=KL, ∠JKL=70°. Find the measure of ∠KLJ. | 498.png | [
"Shape(JK,KL,LJ)"
] | [
"Equal(LengthOfLine(LJ),LengthOfLine(KL))",
"Equal(MeasureOfAngle(JKL),70)"
] | [
"Equal(LengthOfLine(LJ),LengthOfLine(KL))",
"Equal(MeasureOfAngle(JKL),70)"
] | Value(MeasureOfAngle(KLJ)) | 40 | [
"isosceles_triangle_judgment_line_equal(1,LJK)",
"isosceles_triangle_property_angle_equal(1,LJK)",
"triangle_property_angle_sum(1,JKL)"
] | {"START": ["isosceles_triangle_judgment_line_equal(1,LJK)", "triangle_property_angle_sum(1,JKL)"], "isosceles_triangle_judgment_line_equal(1,LJK)": ["isosceles_triangle_property_angle_equal(1,LJK)"]} | |
499 | YimingHe_2023-04-02 | Geometry3k-510 | 6 | 如图所示，BA=BC，BC=1，BC=AC，ED垂直于CD，EDCB是正方形。求三角形ABC的面积与EDCB的面积之比。 | As shown in the diagram, BA=BC, BC=1, BC=AC, ED is perpendicular to CD, quadrilateral EDCB is a square. Find the ratio of the area of triangle ABC to the area of quadrilateral EDCB. | 499.png | [
"Shape(ED,DC,CB,BE)",
"Shape(BC,CA,AB)"
] | [
"Equal(LengthOfLine(BA),LengthOfLine(BC))",
"Equal(LengthOfLine(BC),1)",
"Equal(LengthOfLine(BC),LengthOfLine(AC))",
"PerpendicularBetweenLine(ED,CD)",
"Square(EDCB)"
] | [
"Equal(LengthOfLine(BA),LengthOfLine(BC))",
"Equal(LengthOfLine(BC),LengthOfLine(AC))",
"PerpendicularBetweenLine(ED,CD)"
] | Value(Div(AreaOfTriangle(ABC),AreaOfQuadrilateral(EDCB))) | sqrt(3)/4 | [
"isosceles_triangle_judgment_line_equal(1,ABC)",
"isosceles_triangle_judgment_line_equal(1,BCA)",
"equilateral_triangle_judgment_isosceles_and_isosceles(1,ABC)",
"equilateral_triangle_property_angle(1,ABC)",
"triangle_area_formula_sine(1,ABC)",
"parallelogram_area_formula_sine(1,EDCB)"
] | {"START": ["isosceles_triangle_judgment_line_equal(1,ABC)", "isosceles_triangle_judgment_line_equal(1,BCA)", "triangle_area_formula_sine(1,ABC)", "parallelogram_area_formula_sine(1,EDCB)"], "equilateral_triangle_judgment_isosceles_and_isosceles(1,ABC)": ["equilateral_triangle_property_angle(1,ABC)"], "isosceles_triangl... | |
500 | YimingHe_2023-04-02 | Geometry3k-511 | 6 | 如图所示，⊙A的直径为10，⊙B的直径为30，圆C的直径为10，AD=CH，CH=2，圆A的圆心为A，圆B的圆心为B，C是⊙C的圆心。求直线BX的长度。 | As shown in the diagram, the diameter of circle A is 10, the diameter of circle B is 30, the diameter of ⊙C is 10, AD=CH, CH=2, the center of ⊙A is A, the center of ⊙B is B, C is the center of ⊙C. Find the length of line BX. | 500.png | [
"Shape(ED,BJD,AJE)",
"Shape(DE,AEK,BDK)",
"Shape(DX,AXJ,BJD)",
"Shape(XD,BDK,AKX)",
"Shape(XY,CMY,BMJ,AXJ)",
"Shape(YX,AKX,BKN,CYN)",
"Shape(CMY,YH,BHM)",
"Shape(HY,CYN,BNH)",
"Shape(HF,CFM,BHM)",
"Shape(FH,BNH,CNF)",
"Collinear(EADXBYHCF)",
"Cocircular(A,EKXJ)",
"Cocircular(B,JDKNHM)",
"C... | [
"Equal(DiameterOfCircle(A),10)",
"Equal(DiameterOfCircle(B),30)",
"Equal(DiameterOfCircle(C),10)",
"Equal(LengthOfLine(AD),LengthOfLine(CH))",
"Equal(LengthOfLine(CH),2)",
"IsCentreOfCircle(A,A)",
"IsCentreOfCircle(B,B)",
"IsCentreOfCircle(C,C)"
] | [
"IsCentreOfCircle(A,A)",
"IsCentreOfCircle(B,B)",
"IsCentreOfCircle(C,C)"
] | Value(LengthOfLine(BX)) | 12 | [
"line_addition(1,AD,DX)",
"line_addition(1,DX,XB)",
"radius_of_circle_property_length_equal(1,AX,A)",
"radius_of_circle_property_length_equal(1,BD,B)",
"circle_property_length_of_radius_and_diameter(1,A)",
"circle_property_length_of_radius_and_diameter(1,B)"
] | {"START": ["line_addition(1,AD,DX)", "line_addition(1,DX,XB)", "radius_of_circle_property_length_equal(1,AX,A)", "radius_of_circle_property_length_equal(1,BD,B)", "circle_property_length_of_radius_and_diameter(1,A)", "circle_property_length_of_radius_and_diameter(1,B)"]} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.