SunnyLin/FormalGeo7k_v1 huggingface dataset:
Problem: As shown in the diagram, ∠POM=43°, ON∥PH, PO is parallel to HN. Find the measure of ∠OPH.
问题：如图所示，∠POM=43°，ON∥PH，PO∥HN。求∠OPH的大小。
Construction (CDL):
Shape(KP,PB)
Shape(BP,PO)
Shape(PO,OM)
Shape(MO,OC)
Shape(HP,PK)
Shape(PH,HN,NO,OP)
Shape(CO,ON)
Shape(GH,HP)
Shape(ON,NA)
Shape(FH,HG)
Shape(NH,HF)
Shape(QN,NH)
Shape(AN,NQ)
Collinear(KPOC)
Collinear(GHNA)
Collinear(BPHF)
Collinear(MONQ)
Conditions (CDL):
Equal(MeasureOfAngle(POM),43)
ParallelBetweenLine(ON,PH)
ParallelBetweenLine(PO,HN)
Goal: Value(MeasureOfAngle(OPH))
Answer: 43
Theorem sequence:
adjacent_complementary_angle(1,NOP,POM)
parallel_property_ipsilateral_internal_angle(1,ON,PH)
Problem: As shown in the diagram, AC=y, AD=3, BC=z, CD=x, DB=12, AC⊥BC, CD is perpendicular to AD. Find the value of y.
问题：如图所示，AC=y，AD=3，BC=z，CD=x，DB=12，AC垂直于BC，CD⊥AD。求y的值。
Construction (CDL):
Shape(AC,CD,DA)
Shape(DC,CB,BD)
Collinear(ADB)
Conditions (CDL):
Equal(LengthOfLine(AC),y)
Equal(LengthOfLine(AD),3)
Equal(LengthOfLine(BC),z)
Equal(LengthOfLine(CD),x)
Equal(LengthOfLine(DB),12)
PerpendicularBetweenLine(AC,BC)
PerpendicularBetweenLine(CD,AD)
Goal: Value(y)
Answer: 3*sqrt(5)
Theorem sequence:
line_addition(1,AD,DB)
adjacent_complementary_angle(1,BDC,CDA)
right_triangle_judgment_angle(1,CDA)
right_triangle_judgment_angle(1,BDC)
right_triangle_judgment_angle(1,ACB)
right_triangle_property_pythagorean(1,CDA)
right_triangle_property_pythagorean(1,BDC)
right_triangle_property_pythagorean(1,ACB)
Problem: As shown in the diagram, QR=8, SQ=x, ∠QSR=54°, ∠RQS=37°. Find the value of x.
问题：如图所示，QR=8，SQ=x，∠QSR=54°，∠RQS=37°。求x的值。
Construction (CDL):
Shape(QS,SR,RQ)
Conditions (CDL):
Equal(LengthOfLine(QR),8)
Equal(LengthOfLine(SQ),x)
Equal(MeasureOfAngle(QSR),54)
Equal(MeasureOfAngle(RQS),37)
Goal: Value(x)
Answer: (-8+8*sqrt(5))*cos(pi/180)
Theorem sequence:
triangle_property_angle_sum(1,RQS)
sine_theorem(1,QSR)
Problem: As shown in the diagram, ∠BEC=57°, DF is parallel to GE, FE∥DG. Find the measure of ∠FDG.
问题：如图所示，∠BEC=57°，DF∥GE，FE平行于DG。求∠FDG的大小。
Construction (CDL):
Shape(IF,FA)
Shape(AF,FE)
Shape(FE,EB)
Shape(BE,EC)
Shape(DF,FI)
Shape(CE,EG)
Shape(HD,DF)
Shape(EG,GJ)
Shape(LD,DH)
Shape(GD,DL)
Shape(KG,GD)
Shape(JG,GK)
Shape(FD,DG,GE,EF)
Collinear(AFDL)
Collinear(BEGK)
Collinear(IFEC)
Collinear(HDGJ)
Conditions (CDL):
Equal(MeasureOfAngle(BEC),57)
ParallelBetweenLine(DF,GE)
ParallelBetweenLine(FE,DG)
Goal: Value(MeasureOfAngle(FDG))
Answer: 57
Theorem sequence:
vertical_angle(1,BEC,GEI)
parallelogram_judgment_parallel_and_parallel(1,FDGE)
parallelogram_property_opposite_angle_equal(1,DGEF)
Problem: As shown in the diagram, JV=3, ST=UT, SY=YZ, UJ=9, VJ=3, ZT=18, ZV=UV. Find the length of line YJ.
问题：如图所示，JV=3，ST=UT，SY=YZ，UJ=9，VJ=3，ZT=18，ZV=UV。求直线YJ的长度。
Construction (CDL):
Shape(SY,YJ,JS)
Shape(YZ,ZJ,JY)
Shape(JZ,ZV,VJ)
Shape(JV,VU,UJ)
Shape(JU,UT,TJ)
Shape(JT,TS,SJ)
Collinear(SYZ)
Collinear(SJV)
Collinear(STU)
Collinear(ZJT)
Collinear(ZVU)
Collinear(UJY)
Conditions (CDL):
Equal(LengthOfLine(JV),3)
Equal(LengthOfLine(ST),LengthOfLine(UT))
Equal(LengthOfLine(SY),LengthOfLine(YZ))
Equal(LengthOfLine(UJ),9)
Equal(LengthOfLine(VJ),3)
Equal(LengthOfLine(ZT),18)
Equal(LengthOfLine(ZV),LengthOfLine(UV))
Goal: Value(LengthOfLine(YJ))
Answer: 9/2
Theorem sequence:
median_of_triangle_judgment(1,SV,SZU)
median_of_triangle_judgment(1,ZT,ZUS)
centroid_of_triangle_judgment_intersection(1,J,USZ,T,V)
centroid_of_triangle_property_line_ratio(1,J,USZ,Y)
Problem: As shown in the diagram, ∠ACD=50°, ∠CDA=70°, ∠DBA=21°. Find the measure of ∠BAD.
问题：如图所示，∠ACD=50°，∠CDA=70°，∠DBA=21°。求∠BAD的大小。
Construction (CDL):
Shape(AC,CD,DA)
Shape(AD,DB,BA)
Collinear(CDB)
Conditions (CDL):
Equal(MeasureOfAngle(ACD),50)
Equal(MeasureOfAngle(CDA),70)
Equal(MeasureOfAngle(DBA),21)
Goal: Value(MeasureOfAngle(BAD))
Answer: 49
Theorem sequence:
adjacent_complementary_angle(1,CDA,ADB)
triangle_property_angle_sum(1,ADB)
Problem: As shown in the diagram, ∠ECK=120°, ∠IKH=54°, ∠JKI=36°, HK∥IJ. Find the measure of ∠IJK.
问题：如图所示，∠ECK=120°，∠IKH=54°，∠JKI=36°，HK∥IJ。求∠IJK的大小。
Construction (CDL):
Shape(KH,HI,IK)
Shape(KI,IJ,JK)
Collinear(ECHE)
Conditions (CDL):
Equal(MeasureOfAngle(ECK),120)
Equal(MeasureOfAngle(IKH),54)
Equal(MeasureOfAngle(JKI),36)
ParallelBetweenLine(HK,IJ)
Goal: Value(MeasureOfAngle(IJK))
Answer: 90
Theorem sequence:
triangle_property_angle_sum(1,KHI)
angle_addition(1,HIK,KIJ)
parallel_property_ipsilateral_internal_angle(1,HK,IJ)
triangle_property_angle_sum(1,KIJ)
Problem: As shown in the diagram, MP=10, ∠MPQ=8*x°, ∠QLM=2*x**2-10°, LMPQ is a rhombus. Find the length of line QL.
问题：如图所示，MP=10，∠MPQ=8*x°，∠QLM=2*x**2-10°，四边形LMPQ是菱形。求直线QL的长度。
Construction (CDL):
Shape(LR,RQ,QL)
Shape(RL,LM,MR)
Shape(RM,MP,PR)
Shape(QR,RP,PQ)
Collinear(QRM)
Collinear(LRP)
Conditions (CDL):
Equal(LengthOfLine(MP),10)
Equal(MeasureOfAngle(MPQ),8*x)
Equal(MeasureOfAngle(QLM),2*x**2-10)
Rhombus(LMPQ)
Goal: Value(LengthOfLine(QL))
Answer: 10
Theorem sequence:
Problem: As shown in the diagram, GD=10, HD=HG, HF is perpendicular to DF. Find the length of line DF.
问题：如图所示，GD=10，HD=HG，HF垂直于DF。求直线DF的长度。
Construction (CDL):
Shape(HG,GF,FH)
Shape(HF,FD,DH)
Collinear(DFG)
Conditions (CDL):
Equal(LengthOfLine(GD),10)
Equal(LengthOfLine(HD),LengthOfLine(HG))
PerpendicularBetweenLine(HF,DF)
Goal: Value(LengthOfLine(DF))
Answer: 5
Theorem sequence:
adjacent_complementary_angle(1,GFH,HFD)
isosceles_triangle_judgment_line_equal(1,HGD)
altitude_of_triangle_judgment(1,HF,HGD)
isosceles_triangle_property_line_coincidence(1,HGD,F)
line_addition(1,DF,FG)
Problem: As shown in the diagram, BA=5*x, BC=3*y-4, DA=29, DC=25, ∠ADB=34°, ∠CAD=49°, ∠DCA=54°, quadrilateral ADCB is a parallelogram. Find the measure of ∠CBF.
问题：如图所示，BA=5*x，BC=3*y-4，DA=29，DC=25，∠ADB=34°，∠CAD=49°，∠DCA=54°，四边形ADCB是▱。求∠CBF的大小。
Construction (CDL):
Shape(FC,CB,BF)
Shape(AF,FB,BA)
Shape(FA,AD,DF)
Shape(FD,DC,CF)
Collinear(BFD)
Collinear(AFC)
Conditions (CDL):
Equal(LengthOfLine(BA),5*x)
Equal(LengthOfLine(BC),3*y-4)
Equal(LengthOfLine(DA),29)
Equal(LengthOfLine(DC),25)
Equal(MeasureOfAngle(ADB),34)
Equal(MeasureOfAngle(CAD),49)
Equal(MeasureOfAngle(DCA),54)
Parallelogram(ADCB)
Goal: Value(MeasureOfAngle(CBF))
Answer: 34
Theorem sequence:
parallel_property_alternate_interior_angle(1,DA,CB)
Problem: As shown in the diagram, RS=25, TR=30, TS⊥RS. Find the measure of ∠RTS.
问题：如图所示，RS=25，TR=30，TS垂直于RS。求∠RTS的大小。
Construction (CDL):
Shape(TS,SR,RT)
Conditions (CDL):
Equal(LengthOfLine(RS),25)
Equal(LengthOfLine(TR),30)
PerpendicularBetweenLine(TS,RS)
Goal: Value(MeasureOfAngle(RTS))
Answer: 180*asin(5/6)/pi
Theorem sequence:
sine_theorem(1,RTS)
Problem: As shown in the diagram, AB=c, CA=b, CB=a, ∠ABC=60°, ∠CAB=30°, c=8, BC⊥AC. Find the value of b.
问题：如图所示，AB=c，CA=b，CB=a，∠ABC=60°，∠CAB=30°，c=8，BC⊥AC。求b的值。
Construction (CDL):
Shape(BC,CA,AB)
Conditions (CDL):
Equal(LengthOfLine(AB),c)
Equal(LengthOfLine(CA),b)
Equal(LengthOfLine(CB),a)
Equal(MeasureOfAngle(ABC),60)
Equal(MeasureOfAngle(CAB),30)
Equal(c,8)
PerpendicularBetweenLine(BC,AC)
Goal: Value(b)
Answer: 4*sqrt(3)
Theorem sequence:
sine_theorem(1,ABC)
Problem: As shown in the diagram, AE=4*y, BE=3*y+4, CE=x, DE=2/3*x, AB and CD are opposite sides of the parallelogram ACDB. Find the value of x.
问题：如图所示，AE=4*y，BE=3*y+4，CE=x，DE=2/3*x，AB和CD是▱ACDB的一组对边。求x的值。
Construction (CDL):
Shape(AE,EB,BA)
Shape(AC,CE,EA)
Shape(EC,CD,DE)
Shape(ED,DB,BE)
Collinear(AED)
Collinear(CEB)
Conditions (CDL):
Equal(LengthOfLine(AE),4*y)
Equal(LengthOfLine(BE),3*y+4)
Equal(LengthOfLine(CE),x)
Equal(LengthOfLine(DE),2/3*x)
Parallelogram(ACDB)
Goal: Value(x)
Answer: 8
Theorem sequence:
parallelogram_property_diagonal_bisection(1,ACDB,E)
parallelogram_property_diagonal_bisection(1,CDBA,E)
Problem: As shown in the diagram, AB=x, AC=y, BC=16*sqrt(3), ∠BCA=60°, CA is perpendicular to BA. Find the value of x.
问题：如图所示，AB=x，AC=y，BC=16*sqrt(3)，∠BCA=60°，CA垂直于BA。求x的值。
Construction (CDL):
Shape(CA,AB,BC)
Conditions (CDL):
Equal(LengthOfLine(AB),x)
Equal(LengthOfLine(AC),y)
Equal(LengthOfLine(BC),16*sqrt(3))
Equal(MeasureOfAngle(BCA),60)
PerpendicularBetweenLine(CA,BA)
Goal: Value(x)
Answer: 24
Theorem sequence:
sine_theorem(1,BCA)
Problem: As shown in the diagram, AC=b, CB=a, EA=y, EB=x, ∠CAB=30°, ∠EBC=60°, x=7*sqrt(3), AE⊥CE, BC is perpendicular to AC. Find the value of a.
问题：如图所示，AC=b，CB=a，EA=y，EB=x，∠CAB=30°，∠EBC=60°，x=7*sqrt(3)，AE⊥CE，BC垂直于AC。求a的值。
Construction (CDL):
Shape(BC,CE,EB)
Shape(EC,CA,AE)
Collinear(BEA)
Conditions (CDL):
Equal(LengthOfLine(AC),b)
Equal(LengthOfLine(CB),a)
Equal(LengthOfLine(EA),y)
Equal(LengthOfLine(EB),x)
Equal(MeasureOfAngle(CAB),30)
Equal(MeasureOfAngle(EBC),60)
Equal(x,7*sqrt(3))
PerpendicularBetweenLine(AE,CE)
PerpendicularBetweenLine(BC,AC)
Goal: Value(a)
Answer: 14*sqrt(3)
Theorem sequence:
adjacent_complementary_angle(1,AEC,CEB)
triangle_property_angle_sum(1,CEB)
sine_theorem(1,BCE)
Problem: As shown in the diagram, AC=2*x+9, BD=4*x-5, ∠CAE=42°, ∠DCE=4*y°, ∠EAB=23°, ∠EBD=83°, AC and BD are opposite sides of the parallelogram ABDC. Find the value of y.
问题：如图所示，AC=2*x+9，BD=4*x-5，∠CAE=42°，∠DCE=4*y°，∠EAB=23°，∠EBD=83°，四边形ABDC是平行四边形。求y的值。
Construction (CDL):
Shape(CE,ED,DC)
Shape(AE,EC,CA)
Shape(EA,AB,BE)
Shape(EB,BD,DE)
Collinear(CEB)
Collinear(AED)
Conditions (CDL):
Equal(LengthOfLine(AC),2*x+9)
Equal(LengthOfLine(BD),4*x-5)
Equal(MeasureOfAngle(CAE),42)
Equal(MeasureOfAngle(DCE),4*y)
Equal(MeasureOfAngle(EAB),23)
Equal(MeasureOfAngle(EBD),83)
Parallelogram(ABDC)
Goal: Value(y)
Answer: 8
Theorem sequence:
parallel_property_alternate_interior_angle(1,AC,BD)
parallel_property_alternate_interior_angle(1,BA,DC)
angle_addition(1,ABE,EBD)
triangle_property_angle_sum(1,ABD)
Problem: As shown in the diagram, ∠WZY=4*x°, ∠XWZ=3*x°, ∠YXW=x°, ∠ZYX=2*x°. Find the measure of ∠WZY.
问题：如图所示，∠WZY=4*x°，∠XWZ=3*x°，∠YXW=x°，∠ZYX=2*x°。求∠WZY的大小。
Construction (CDL):
Shape(XW,WZ,ZY,YX)
Conditions (CDL):
Equal(MeasureOfAngle(WZY),4*x)
Equal(MeasureOfAngle(XWZ),3*x)
Equal(MeasureOfAngle(YXW),x)
Equal(MeasureOfAngle(ZYX),2*x)
Goal: Value(MeasureOfAngle(WZY))
Answer: 144
Theorem sequence:
quadrilateral_property_angle_sum(1,XWZY)
Problem: As shown in the diagram, ∠ANC=30°, ∠CEB=110°, ∠ENI=130°, ∠NCF=∠AFN. Find the measure of ∠FNA.
问题：如图所示，∠ANC=30°，∠CEB=110°，∠ENI=130°，∠NCF=∠AFN。求∠FNA的大小。
Construction (CDL):
Shape(CA,AE,EC)
Shape(EA,AN,NE)
Shape(AF,FN,NA)
Shape(CE,EB)
Shape(BE,EN)
Shape(EN,NI)
Collinear(AEB)
Collinear(FNI)
Collinear(CEN)
Collinear(CAF)
Conditions (CDL):
Equal(MeasureOfAngle(ANC),30)
Equal(MeasureOfAngle(CEB),110)
Equal(MeasureOfAngle(ENI),130)
Equal(MeasureOfAngle(NCF),MeasureOfAngle(AFN))
Goal: Value(MeasureOfAngle(FNA))
Answer: 20
Theorem sequence:
angle_addition(1,ANE,ENI)
adjacent_complementary_angle(1,FNA,ANI)
Problem: As shown in the diagram, AC=53, BC=68, ∠ABC=48°, ∠CAB=x°, x=72. Find the length of line AB.
问题：如图所示，AC=53，BC=68，∠ABC=48°，∠CAB=x°，x=72。求直线AB的长度。
Construction (CDL):
Shape(AB,BC,CA)
Conditions (CDL):
Equal(LengthOfLine(AC),53)
Equal(LengthOfLine(BC),68)
Equal(MeasureOfAngle(ABC),48)
Equal(MeasureOfAngle(CAB),x)
Equal(x,72)
Goal: Value(LengthOfLine(AB))
Answer: sqrt(3829)
Theorem sequence:
triangle_property_angle_sum(1,ABC)
cosine_theorem(1,CAB)
Problem: As shown in the diagram, ∠DHG=2*x+11°, ∠GFD=2*y°, ∠HGF=x-5°, DF and HG are opposite sides of the parallelogram FDHG. Find the value of y.
问题：如图所示，∠DHG=2*x+11°，∠GFD=2*y°，∠HGF=x-5°，FDHG是平行四边形。求y的值。
Construction (CDL):
Shape(FD,DH,HG,GF)
Conditions (CDL):
Equal(MeasureOfAngle(DHG),2*x+11)
Equal(MeasureOfAngle(GFD),2*y)
Equal(MeasureOfAngle(HGF),x-5)
Parallelogram(FDHG)
Goal: Value(y)
Answer: 127/2
Theorem sequence:
parallel_property_ipsilateral_internal_angle(1,FG,DH)
parallel_property_ipsilateral_internal_angle(1,HD,GF)
parallel_property_ipsilateral_internal_angle(1,DF,HG)
Problem: As shown in the diagram, XN=10, YN=5/2, XZ⊥YZ, ZN⊥XN. Find the height of △ZYX.
问题：如图所示，XN=10，YN=5/2，XZ⊥YZ，ZN⊥XN。求三角形ZYX的高。
Construction (CDL):
Shape(ZY,YN,NZ)
Shape(ZN,NX,XZ)
Collinear(YNX)
Conditions (CDL):
Equal(LengthOfLine(XN),10)
Equal(LengthOfLine(YN),5/2)
PerpendicularBetweenLine(XZ,YZ)
PerpendicularBetweenLine(ZN,XN)
Goal: Value(HeightOfTriangle(ZYX))
Answer: 5
Theorem sequence:
line_addition(1,YN,NX)
adjacent_complementary_angle(1,YNZ,ZNX)
right_triangle_judgment_angle(1,YNZ)
right_triangle_judgment_angle(1,ZNX)
right_triangle_judgment_angle(1,XZY)
right_triangle_property_pythagorean(1,YNZ)
right_triangle_property_pythagorean(1,ZNX)
right_triangle_property_pythagorean(1,XZY)
altitude_of_triangle_judgment(1,ZN,ZYX)
Problem: As shown in the diagram, VW=3*x-6, WX=x+4, YW=5, ZW=6, ZV is parallel to XY. Find the value of x.
问题：如图所示，VW=3*x-6，WX=x+4，YW=5，ZW=6，ZV∥XY。求x的值。
Construction (CDL):
Shape(VZ,ZW,WV)
Shape(XY,YW,WX)
Collinear(VWX)
Collinear(ZWY)
Conditions (CDL):
Equal(LengthOfLine(VW),3*x-6)
Equal(LengthOfLine(WX),x+4)
Equal(LengthOfLine(YW),5)
Equal(LengthOfLine(ZW),6)
ParallelBetweenLine(ZV,XY)
Goal: Value(x)
Answer: 6
Theorem sequence:
parallel_property_alternate_interior_angle(2,ZV,XY)
vertical_angle(1,ZWV,YWX)
similar_triangle_judgment_aa(1,ZWV,YWX)
similar_triangle_property_line_ratio(1,ZWV,YWX)
similar_triangle_property_line_ratio(1,VZW,XYW)
Problem: As shown in the diagram, ∠ABC=y+3°, ∠BAD=2*x+6°, ∠CDB=2*y+5°, ∠DCA=4*y-9°, BD and CA are opposite sides of the parallelogram BCAD. Find the value of x.
问题：如图所示，∠ABC=y+3°，∠BAD=2*x+6°，∠CDB=2*y+5°，∠DCA=4*y-9°，四边形BCAD是▱。求x的值。
Construction (CDL):
Shape(BE,ED,DB)
Shape(BC,CE,EB)
Shape(EC,CA,AE)
Shape(EA,AD,DE)
Collinear(CED)
Collinear(BEA)
Conditions (CDL):
Equal(MeasureOfAngle(ABC),y+3)
Equal(MeasureOfAngle(BAD),2*x+6)
Equal(MeasureOfAngle(CDB),2*y+5)
Equal(MeasureOfAngle(DCA),4*y-9)
Parallelogram(BCAD)
Goal: Value(x)
Answer: 2
Theorem sequence:
parallel_property_alternate_interior_angle(2,BD,CA)
parallel_property_alternate_interior_angle(2,CB,AD)
Problem: As shown in the diagram, Add(MeasureOfAngle(BAE)=MeasureOfAngle(CAD)), ∠CAD=47°. Find the measure of ∠BAE.
问题：如图所示，Add(MeasureOfAngle(BAE)=MeasureOfAngle(CAD))，∠CAD=47°。求∠BAE的大小。
Construction (CDL):
Shape(BA,AE)
Shape(DA,AB)
Shape(CA,AD)
Collinear(EAC)
Conditions (CDL):
Equal(Add(MeasureOfAngle(BAE),MeasureOfAngle(CAD)),90)
Equal(MeasureOfAngle(CAD),47)
Goal: Value(MeasureOfAngle(BAE))
Answer: 43
Theorem sequence:
Problem: As shown in the diagram, EH=HG, ∠HGE=3*x+6°, EH⊥GH. Find the value of x.
问题：如图所示，EH=HG，∠HGE=3*x+6°，EH垂直于GH。求x的值。
Construction (CDL):
Shape(EH,HG,GE)
Conditions (CDL):
Equal(LengthOfLine(EH),LengthOfLine(HG))
Equal(MeasureOfAngle(HGE),3*x+6)
PerpendicularBetweenLine(EH,GH)
Goal: Value(x)
Answer: 13
Theorem sequence:
triangle_property_angle_sum(1,HGE)
isosceles_triangle_judgment_line_equal(1,HGE)
isosceles_triangle_property_angle_equal(1,HGE)
Problem: As shown in the diagram, AF=x, BD=20, CD=DX, EF=FG, EG=12, XC=16, ∠BCX=∠EGA, ∠CXB=∠AEG. Find the value of x.
问题：如图所示，AF=x，BD=20，CD=DX，EF=FG，EG=12，XC=16，∠BCX=∠EGA，∠CXB=∠AEG。求x的值。
Construction (CDL):
Shape(BC,CD,DB)
Shape(BD,DX,XB)
Shape(AE,EF,FA)
Shape(AF,FG,GA)
Collinear(CDX)
Collinear(EFG)
Conditions (CDL):
Equal(LengthOfLine(AF),x)
Equal(LengthOfLine(BD),20)
Equal(LengthOfLine(CD),LengthOfLine(DX))
Equal(LengthOfLine(EF),LengthOfLine(FG))
Equal(LengthOfLine(EG),12)
Equal(LengthOfLine(XC),16)
Equal(MeasureOfAngle(BCX),MeasureOfAngle(EGA))
Equal(MeasureOfAngle(CXB),MeasureOfAngle(AEG))
Goal: Value(x)
Answer: 15
Theorem sequence:
line_addition(1,CD,DX)
line_addition(1,EF,FG)
mirror_similar_triangle_judgment_aa(1,BCX,AEG)
mirror_similar_triangle_property_line_ratio(1,BCX,AEG)
mirror_similar_triangle_property_line_ratio(1,CXB,GAE)
mirror_similar_triangle_judgment_sas(1,XBD,EFA)
mirror_similar_triangle_property_line_ratio(1,XBD,EFA)
mirror_similar_triangle_property_line_ratio(1,BDX,AEF)
Problem: As shown in the diagram, ∠TVU=x°, the measure of arc BRS is 84, the measure of arc BUT is 130, B is the center of ⊙B. Find the value of x.
问题：如图所示，∠TVU=x°，弧BRS的角度为84，⌒BUT的角度为130，圆B的圆心为B。求x的值。
Construction (CDL):
Shape(SV,VR,BRS)
Shape(VS,SU,UV)
Shape(US,BSU)
Shape(VU,BUT,TV)
Shape(RV,VT,BTR)
Collinear(RVU)
Collinear(SVT)
Cocircular(B,RSUT)
Conditions (CDL):
Equal(MeasureOfAngle(TVU),x)
Equal(MeasureOfArc(BRS),84)
Equal(MeasureOfArc(BUT),130)
IsCentreOfCircle(B,B)
Goal: Value(x)
Answer: 107
Theorem sequence:
arc_property_circumference_angle_external(1,BRS,U)
arc_property_circumference_angle_external(1,BUT,S)
triangle_property_angle_sum(1,VSU)
vertical_angle(1,RVT,UVS)
adjacent_complementary_angle(1,RVT,TVU)
Problem: As shown in the diagram, the area of the ⊙A is 20*pi. Find the circumference of the circle A.
问题：如图所示，⊙A的面积为20*pi。求圆A的周长。
Construction (CDL):
Cocircular(A)
Conditions (CDL):
Equal(AreaOfCircle(A),20*pi)
Goal: Value(PerimeterOfCircle(A))
Answer: 4*sqrt(5)*pi
Theorem sequence:
circle_area_formula(1,A)
circle_perimeter_formula(1,A)
Problem: As shown in the diagram, ∠PMQ=72°, the center of circle O is O, QM is the tangent to ⊙O. Find the measure of arc OMP.
问题：如图所示，∠PMQ=72°，O是圆O的圆心，圆O的切线为QM。求⌒OMP的角度。
Construction (CDL):
Shape(OP,OPM,MO)
Shape(OM,MP,PO)
Shape(PM,OMP)
Shape(PM,MQ)
Cocircular(O,PM)
Conditions (CDL):
Equal(MeasureOfAngle(PMQ),72)
IsCentreOfCircle(O,O)
IsTangentOfCircle(QM,O)
Goal: Value(MeasureOfArc(OMP))
Answer: 144
Theorem sequence:
tangent_of_circle_property_perpendicular(1,QM,O,O)
angle_addition(1,OMP,PMQ)
radius_of_circle_property_length_equal(1,OP,O)
radius_of_circle_property_length_equal(1,OM,O)
isosceles_triangle_judgment_line_equal(1,OMP)
isosceles_triangle_property_angle_equal(1,OMP)
triangle_property_angle_sum(1,OMP)
arc_property_center_angle(1,OMP,O)
Problem: As shown in the diagram, QP=8, QR=x, SR=7, QP is the tangent to circle B. Find the value of x.
问题：如图所示，QP=8，QR=x，SR=7，⊙O的切线为QP。求x的值。
Construction (CDL):
Shape(SR,BRS)
Shape(RS,BSR)
Shape(RQ,QP,BRP)
Collinear(SRQ)
Cocircular(B,SRP)
Conditions (CDL):
Equal(LengthOfLine(QP),8)
Equal(LengthOfLine(QR),x)
Equal(LengthOfLine(SR),7)
IsTangentOfCircle(QP,B)
Goal: Value(x)
Answer: -7/2+sqrt(305)/2
Theorem sequence:
circle_property_circular_power_tangent_and_segment_line(1,QP,QRS,B)
line_addition(1,SR,RQ)
Problem: As shown in the diagram, ∠ABC=1/2*y°, ∠BDC=3*y-4°, ∠CAB=4*x-8°, ∠DCB=x-12°, CD and AB are opposite sides of the ▱ CABD. Find the value of y.
问题：如图所示，∠ABC=1/2*y°，∠BDC=3*y-4°，∠CAB=4*x-8°，∠DCB=x-12°，CD和AB是平行四边形CABD的一组对边。求y的值。
Construction (CDL):
Shape(AB,BC,CA)
Shape(CB,BD,DC)
Conditions (CDL):
Equal(MeasureOfAngle(ABC),1/2*y)
Equal(MeasureOfAngle(BDC),3*y-4)
Equal(MeasureOfAngle(CAB),4*x-8)
Equal(MeasureOfAngle(DCB),x-12)
Parallelogram(CABD)
Goal: Value(y)
Answer: 44
Theorem sequence:
parallel_property_alternate_interior_angle(1,CD,AB)
parallelogram_property_opposite_angle_equal(1,ABDC)
Problem: As shown in the diagram, AE=4*sqrt(3), ∠DAE=30°, AE is perpendicular to DE, quadrilateral ADCB is a square. Find the area of quadrilateral ADCB.
问题：如图所示，AE=4*sqrt(3)，∠DAE=30°，AE垂直于DE，ADCB是正方形。求ADCB的面积。
Construction (CDL):
Shape(AE,ED,DA)
Shape(AD,DC,CB,BA)
Conditions (CDL):
Equal(LengthOfLine(AE),4*sqrt(3))
Equal(MeasureOfAngle(DAE),30)
PerpendicularBetweenLine(AE,DE)
Square(ADCB)
Goal: Value(AreaOfQuadrilateral(ADCB))
Answer: 64
Theorem sequence:
triangle_property_angle_sum(1,AED)
sine_theorem(1,AED)
parallelogram_area_formula_sine(1,ADCB)
Problem: As shown in the diagram, AC=19, BN=10, EF=2, NC=20, AF is the height of quadrilateral AEBC, AF⊥NF, FN is perpendicular to CN, AE and BC are the non-parallel sides (legs) of trapezoid AEBC. Find the area of AEBC.
问题：如图所示，AC=19，BN=10，EF=2，NC=20，AF是四边形AEBC的高，AF垂直于NF，FN⊥CN，AE和BC是梯形AEBC的腰。求AEBC的面积。
Construction (CDL):
Shape(EF,FA,AE)
Shape(AF,FN,NC,CA)
Shape(CN,NB,BC)
Collinear(EFNB)
Conditions (CDL):
Equal(LengthOfLine(AC),19)
Equal(LengthOfLine(BN),10)
Equal(LengthOfLine(EF),2)
Equal(LengthOfLine(NC),20)
IsAltitudeOfQuadrilateral(AF,AEBC)
PerpendicularBetweenLine(AF,NF)
PerpendicularBetweenLine(FN,CN)
Trapezoid(AEBC)
Goal: Value(AreaOfQuadrilateral(AEBC))
Answer: 500
Theorem sequence:
parallel_judgment_per_per(1,FA,NC)
parallel_judgment_per_per(1,AC,FN)
parallelogram_judgment_parallel_and_parallel(1,AFNC)
parallelogram_property_opposite_line_equal(1,AFNC)
parallelogram_property_opposite_line_equal(1,FNCA)
line_addition(1,EF,FN)
line_addition(1,EN,NB)
trapezoid_area_formula(1,AEBC)
Problem: As shown in the diagram, ∠BAC=2*x°, ∠DAE=3*x°, ∠EAB=x°. Find the value of x.
问题：如图所示，∠BAC=2*x°，∠DAE=3*x°，∠EAB=x°。求x的值。
Construction (CDL):
Shape(DA,AE)
Shape(EA,AB)
Shape(BA,AC)
Collinear(DAC)
Conditions (CDL):
Equal(MeasureOfAngle(BAC),2*x)
Equal(MeasureOfAngle(DAE),3*x)
Equal(MeasureOfAngle(EAB),x)
Goal: Value(x)
Answer: 30
Theorem sequence:
angle_addition(1,DAE,EAB)
adjacent_complementary_angle(1,DAB,BAC)
Problem: As shown in the diagram, CH=7, EF=11, EH=6, FE=11, FH=10, quadrilateral ADEG is a parallelogram, triangle HBC is similar to triangle HEF.. Find the perimeter of triangle HBC.
问题：如图所示，CH=7，EF=11，EH=6，FE=11，FH=10，DA和EG是平行四边形ADEG的一组对边，三角形HBC与三角形HEF是相似三角形。求三角形HBC的周长。
Construction (CDL):
Shape(CD,DE,EH,HC)
Shape(CH,HB,BC)
Shape(HE,EF,FH)
Shape(BH,HF,FG,GA,AB)
Collinear(BHE)
Collinear(CHF)
Conditions (CDL):
Equal(LengthOfLine(CH),7)
Equal(LengthOfLine(EF),11)
Equal(LengthOfLine(EH),6)
Equal(LengthOfLine(FE),11)
Equal(LengthOfLine(FH),10)
Parallelogram(ADEG)
SimilarBetweenTriangle(HBC,HEF)
Goal: Value(PerimeterOfTriangle(HBC))
Answer: 189/10
Theorem sequence:
similar_triangle_property_line_ratio(1,HBC,HEF)
similar_triangle_property_line_ratio(1,BCH,EFH)
similar_triangle_property_line_ratio(1,CHB,FHE)
triangle_perimeter_formula(1,CHB)
Problem: As shown in the diagram, ∠ANE=30°, ∠CEB=110°, ∠ENI=130°, ∠NCA=∠CFN. Find the measure of ∠CFN.
问题：如图所示，∠ANE=30°，∠CEB=110°，∠ENI=130°，∠NCA=∠CFN。求∠CFN的大小。
Construction (CDL):
Shape(CA,AE,EC)
Shape(EA,AN,NE)
Shape(AF,FN,NA)
Shape(CE,EB)
Shape(EN,NI)
Collinear(AEB)
Collinear(FNI)
Collinear(CAF)
Collinear(CEN)
Conditions (CDL):
Equal(MeasureOfAngle(ANE),30)
Equal(MeasureOfAngle(CEB),110)
Equal(MeasureOfAngle(ENI),130)
Equal(MeasureOfAngle(NCA),MeasureOfAngle(CFN))
Goal: Value(MeasureOfAngle(CFN))
Answer: 65
Theorem sequence:
angle_addition(1,EAN,NAF)
angle_addition(1,ANE,ENI)
adjacent_complementary_angle(1,FNA,ANI)
adjacent_complementary_angle(1,CAE,EAF)
adjacent_complementary_angle(1,NEA,AEC)
triangle_property_angle_sum(1,CAE)
triangle_property_angle_sum(1,EAN)
triangle_property_angle_sum(1,AFN)
Problem: As shown in the diagram, PQ=12, QR=2, TS=3. Find the length of line RS.
问题：如图所示，PQ=12，QR=2，TS=3。求直线RS的长度。
Construction (CDL):
Shape(PQ,AQP)
Shape(QP,APT,TS,ASQ)
Shape(ST,ATS)
Shape(SR,RQ,ASR)
Collinear(PQR)
Collinear(TSR)
Cocircular(A,PTSQ)
Conditions (CDL):
Equal(LengthOfLine(PQ),12)
Equal(LengthOfLine(QR),2)
Equal(LengthOfLine(TS),3)
Goal: Value(LengthOfLine(RS))
Answer: 4
Theorem sequence:
circle_property_circular_power_segment_and_segment_line(1,RQP,RST,A)
line_addition(1,PQ,QR)
line_addition(1,TS,SR)
Problem: As shown in the diagram, ∠TZY=30*x°, ∠TZY=∠ZYW, ∠WTZ=20*x°, ∠WTZ=∠YWT, TZ and YW are the non-parallel sides (legs) of trapezoid TZYW. Find the measure of ∠WTZ.
问题：如图所示，∠TZY=30*x°，∠TZY=∠ZYW，∠WTZ=20*x°，∠WTZ=∠YWT，TZYW是梯形。求∠WTZ的大小。
Construction (CDL):
Shape(TZ,ZY,YW,WT)
Conditions (CDL):
Equal(MeasureOfAngle(TZY),30*x)
Equal(MeasureOfAngle(TZY),MeasureOfAngle(ZYW))
Equal(MeasureOfAngle(WTZ),20*x)
Equal(MeasureOfAngle(WTZ),MeasureOfAngle(YWT))
Trapezoid(TZYW)
Goal: Value(MeasureOfAngle(WTZ))
Answer: 72
Theorem sequence:
quadrilateral_property_angle_sum(1,TZYW)
Problem: As shown in the diagram, AB=9, AD=4*x-8, JK=21, JM=5*x+3, AB is the altitude of triangle ABD, JK is the altitude of triangle JKM, AB⊥CB, JK is perpendicular to LK, △DAC is similar to △MJL.. Find the value of x.
问题：如图所示，AB=9，AD=4*x-8，JK=21，JM=5*x+3，AB是△ABD的高，JK是三角形JKM的高，AB垂直于CB，JK⊥LK，△DAC相似于△MJL。求x的值。
Construction (CDL):
Shape(AB,BC,CA)
Shape(AC,CD,DA)
Shape(JK,KL,LJ)
Shape(JL,LM,MJ)
Collinear(BCD)
Collinear(KLM)
Conditions (CDL):
Equal(LengthOfLine(AB),9)
Equal(LengthOfLine(AD),4*x-8)
Equal(LengthOfLine(JK),21)
Equal(LengthOfLine(JM),5*x+3)
IsAltitudeOfTriangle(AB,ABD)
IsAltitudeOfTriangle(JK,JKM)
PerpendicularBetweenLine(AB,CB)
PerpendicularBetweenLine(JK,LK)
SimilarBetweenTriangle(DAC,MJL)
Goal: Value(x)
Answer: 5
Theorem sequence:
similar_triangle_property_angle_equal(1,DAC,MJL)
similar_triangle_judgment_aa(1,ABD,JKM)
similar_triangle_property_line_ratio(1,DAB,MJK)
similar_triangle_property_line_ratio(1,BDA,KMJ)