images images listlengths 1 1 | problem stringlengths 310 675 | answer stringlengths 114 1.18k | proID stringlengths 1 4 |
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<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BFC=35°, ∠CED=35°, the center of ⊙O is O. Find the measure of ∠DAB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then pro... | consCDL:['Shape(OAB,BA)', 'Shape(OBC,CB)', 'Shape(OCD,DC)', 'Shape(ODA,AD)', 'Shape(AB,BC,CD,DA)', 'Shape(OBC,BF,FC)', 'Shape(OCD,CE,ED)', 'Collinear(ADE)', 'Collinear(ABF)', 'Collinear(DCF)', 'Collinear(ECB)', 'Cocircular(O,ABCD)'], imgCDL:['Equal(MeasureOfAngle(BFC),35)', 'Equal(MeasureOfAngle(CED),35)'], textCDL:['E... | 4515 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DCE=70°, the center of ⊙O is O. Find the measure of ∠DFB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all C... | consCDL:['Shape(OFB,BF)', 'Shape(ODF,FD)', 'Shape(OBC,CB)', 'Shape(OCD,DC)', 'Shape(FB,BC,CD,DF)', 'Shape(CE)', 'Collinear(BCE)', 'Cocircular(O,FBCD)'], imgCDL:['Equal(MeasureOfAngle(DCE),70)'], textCDL:['Equal(MeasureOfAngle(DCE),70)', 'IsCentreOfCircle(O,O)']. | 4525 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DOB=138°, O is the center of ⊙O. Find the measure of ∠DCE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all ... | consCDL:['Shape(BA,OAB)', 'Shape(AB,BO,OD,DA)', 'Shape(OB,BC,CD,DO)', 'Shape(CB,OBC)', 'Shape(DC,OCD)', 'Shape(AD,ODA)', 'Shape(CE)', 'Collinear(BCE)', 'Cocircular(O,ABCD)'], imgCDL:['Equal(MeasureOfAngle(DOB),138)'], textCDL:['Equal(MeasureOfAngle(DOB),138)', 'IsCentreOfCircle(O,O)']. | 4542 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠COA=160°, the center of circle O is O. Find the measure of ∠ADC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provid... | consCDL:['Shape(AB,OBA)', 'Shape(BA,AO,OC,CB)', 'Shape(BC,OCB)', 'Shape(OA,AC,CO)', 'Shape(DA,OAD)', 'Shape(AD,DC,CA)', 'Shape(CD,ODC)', 'Cocircular(O,ADCB)'], imgCDL:['Equal(MeasureOfAngle(COA),160)'], textCDL:['Equal(MeasureOfAngle(COA),160)', 'IsCentreOfCircle(O,O)']. | 4559 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=8, AH=6, the radius of circle O is 5, O is the center of circle O, AH⊥CH. Find the length of line AB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think with... | consCDL:['Shape(AB,BH,HA)', 'Shape(AH,HO,OA)', 'Shape(AO,OC,CA)', 'Shape(OH,HM,MO)', 'Shape(OM,MC,CO)', 'Shape(ME,EC,CM)', 'Shape(OAB,BA)', 'Shape(MH,HB,OBE,EM)', 'Shape(CE,OEC)', 'Shape(AC,OCA)', 'Collinear(AOME)', 'Collinear(BHMC)', 'Cocircular(O,ABEC)'], imgCDL:['Equal(LengthOfLine(AC),8)', 'Equal(LengthOfLine(AH),6... | 4599 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=13, AC=5, BC=12, O is the center of circle O, the tangent to ⊙O is BM. Find the length of line PQ. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within ... | consCDL:['Shape(BQ,OMQ,MB)', 'Shape(OMQ,QO,OM)', 'Shape(QC,CO,OQ)', 'Shape(OQC,CQ)', 'Shape(OC,CP,PO)', 'Shape(PC,OCP)', 'Shape(MO,OP,OPM)', 'Shape(OPM,PA,AM)', 'Collinear(POQ)', 'Collinear(COM)', 'Collinear(BQC)', 'Collinear(CPA)', 'Collinear(AMB)', 'Cocircular(O,CPMQ)'], imgCDL:['Equal(LengthOfLine(AB),13)', 'Equal(L... | 4624 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ADC=32°, the center of circle O is O, BA is the tangent to circle O. Find ∠OBA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags ... | consCDL:['Shape(DM,MO,OA,OAD)', 'Shape(DC,CM,MD)', 'Shape(OM,MA,AO)', 'Shape(MC,OCA,AM)', 'Shape(CD,ODC)', 'Shape(OCA,CB,BA)', 'Collinear(DMA)', 'Collinear(OMCB)', 'Cocircular(O,DCA)'], imgCDL:['Equal(MeasureOfAngle(ADC),32)'], textCDL:['Equal(MeasureOfAngle(ADC),32)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(BA,O)'... | 4628 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, the perimeter of triangle ACB is 24, the center of ⊙O is O, the tangent to ⊙O is AD, the tangent to ⊙O is AE, BF is the tangent to circle O, the tangent to circle O is CF. Find AD. Please provide the consCDL and imgCDL based on this given geometri... | consCDL:['Shape(AC,CF,FB,BA)', 'Shape(FC,CE,OFE)', 'Shape(BF,ODF,DB)', 'Shape(OFE,EO,OF)', 'Shape(ODF,FO,OD)', 'Shape(DO,OE,OED)', 'Collinear(ACE)', 'Collinear(ABD)', 'Collinear(CFB)', 'Cocircular(O,DFE)'], imgCDL:[], textCDL:['Equal(PerimeterOfTriangle(ACB),24)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(AD,O)', 'Is... | 4637 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BCD=25°, the center of ⊙O is O, DC is the tangent to circle O. Find ∠CBO. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and th... | consCDL:['Shape(OC,CB,BO)', 'Shape(OCB,BC)', 'Shape(CD)', 'Shape(OBC,CO,OB)', 'Cocircular(O,CB)'], imgCDL:['Equal(MeasureOfAngle(BCD),25)'], textCDL:['Equal(MeasureOfAngle(BCD),25)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(DC,O)']. | 4666 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠APO=36°, the center of circle O is O, AB is the diameter of circle O, the tangent to ⊙O is PA. Find ∠CBA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think wi... | consCDL:['Shape(AP,PC,OAC)', 'Shape(OA,OAC,CO)', 'Shape(OC,CB,OCB)', 'Collinear(AOB)', 'Collinear(PCO)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(APO),36)'], textCDL:['Equal(MeasureOfAngle(APO),36)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)', 'IsTangentOfCircle(PA,O)']. | 4670 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, PC=3, ∠CAP=30°, △DOC is an equilateral △, O is the center of circle O, the diameter of circle O is AB, PC is the tangent to circle O, OE is perpendicular to AE. Find the length of line CD. Please provide the consCDL and imgCDL based on this given ... | consCDL:['Shape(EA,AO,OE)', 'Shape(DE,EC,CD)', 'Shape(OCD,DC)', 'Shape(EO,OC,CE)', 'Shape(ED,ODA,AE)', 'Shape(OA,OAB,BO)', 'Shape(OBC,BP,PC)', 'Collinear(AOBP)', 'Collinear(DEO)', 'Collinear(AEC)', 'Cocircular(O,DABC)'], imgCDL:['Equal(LengthOfLine(PC),3)', 'Equal(MeasureOfAngle(CAP),30)', 'PerpendicularBetweenLine(OE,... | 4672 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=5, AC=3, the center of circle O is O, AC is the tangent to ⊙O, AP is the tangent to ⊙O, the tangent to ⊙O is BD, BP is the tangent to circle O. Find the length of line BD. Please provide the consCDL and imgCDL based on this given geometric diag... | consCDL:['Shape(CA,AP,OCP)', 'Shape(PB,BD,OPD)', 'Shape(OCP,OPD,ODC)', 'Collinear(APB)', 'Cocircular(O,CPD)'], imgCDL:['Equal(LengthOfLine(AB),5)', 'Equal(LengthOfLine(AC),3)'], textCDL:['Equal(LengthOfLine(AB),5)', 'Equal(LengthOfLine(AC),3)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(AC,O)', 'IsTangentOfCircle(AP,O... | 4675 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=4, BF=5, CD=9, CF=AD, ∠CFB=90°, the center of circle O is O, AD is the diameter of circle O, the tangent to ⊙O is BA, BE is the tangent to circle O, the tangent to circle O is CD, the tangent to circle O is CE. Find Radius(⊙O). Please provide t... | consCDL:['Shape(EB,BA,OEA)', 'Shape(ODE,DC,CE)', 'Shape(BE,EC,CF,FB)', 'Shape(OD,ODE,OEA,AO)', 'Collinear(AOD)', 'Collinear(BEC)', 'Collinear(ABF)', 'Cocircular(O,DEA)'], imgCDL:['Equal(LengthOfLine(AB),4)', 'Equal(LengthOfLine(BF),5)', 'Equal(LengthOfLine(CD),9)', 'Equal(LengthOfLine(CF),LengthOfLine(AD))', 'Equal(Mea... | 4676 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, EA=AF, ∠OEF=40°, O is the center of ⊙O, the tangent to ⊙O is EA, the tangent to ⊙O is FA. Find ∠DBC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <... | consCDL:['Shape(OC,OCA,AO)', 'Shape(OA,OAD,DO)', 'Shape(CE,EA,OCA)', 'Shape(OAD,AF,FD)', 'Shape(OBC,CB)', 'Shape(ODB,BD)', 'Shape(BC,CO,OD,DB)', 'Collinear(EAF)', 'Collinear(ODF)', 'Collinear(OCE)', 'Cocircular(O,BCAD)'], imgCDL:['Equal(LengthOfLine(EA),LengthOfLine(AF))', 'Equal(MeasureOfAngle(OEF),40)'], textCDL:['Eq... | 4680 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ⌒ODC is congruent to ⌒OCE, ∠BAC=50°, O is the center of ⊙O, the diameter of ⊙O is BC, AC is the tangent to ⊙O, the tangent to circle O is FC, the tangent to circle O is FE. Find ∠CFE. Please provide the consCDL and imgCDL based on this given geome... | consCDL:['Shape(DB,OBD)', 'Shape(CO,OB,BD,ODC)', 'Shape(DA,AC,ODC)', 'Shape(BO,OE,OEB)', 'Shape(EO,OC,OCE)', 'Shape(CF,FE,OCE)', 'Collinear(ACF)', 'Collinear(ADB)', 'Collinear(BOC)', 'Cocircular(O,BDCE)'], imgCDL:['Equal(MeasureOfAngle(BAC),50)'], textCDL:['CongruentBetweenArc(ODC,OCE)', 'Equal(MeasureOfAngle(BAC),50)'... | 4706 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠APC=40°, the center of ⊙O is O, PA is the tangent to circle O. Find the measure of ∠CBO. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></thi... | consCDL:['Shape(CO,OA,OAC)', 'Shape(OC,CB,BO)', 'Shape(BC,OCB)', 'Shape(AO,OB,OBA)', 'Shape(AP,PC,OAC)', 'Collinear(AOB)', 'Collinear(PCO)', 'Cocircular(O,BAC)'], imgCDL:['Equal(MeasureOfAngle(APC),40)'], textCDL:['Equal(MeasureOfAngle(APC),40)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(PA,O)']. | 4744 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠APB=70°, O is the center of ⊙O, PA is the tangent to ⊙O, the tangent to circle O is PB. Find the measure of ∠ACB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first ... | consCDL:['Shape(AP,PB,OCB,OAC)', 'Shape(OAC,CA)', 'Shape(OCB,BC)', 'Shape(OA,AC,CB,BO)', 'Shape(OB,BD,DA,AO)', 'Shape(DB,OBD)', 'Shape(AD,ODA)', 'Cocircular(O,ACBD)'], imgCDL:['Equal(MeasureOfAngle(APB),70)'], textCDL:['Equal(MeasureOfAngle(APB),70)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(PA,O)', 'IsTangentOfCirc... | 4826 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠OBA=32°, O is the center of circle O, the tangent to circle O is BA. Find the measure of ∠ADC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think... | consCDL:['Shape(CB,BA,OCA)', 'Shape(OCA,AM,MC)', 'Shape(MA,AO,OM)', 'Shape(ODC,CD)', 'Shape(DC,CM,MD)', 'Shape(DM,MO,OA,OAD)', 'Collinear(BCMO)', 'Collinear(DMA)', 'Cocircular(O,DCA)'], imgCDL:['Equal(MeasureOfAngle(OBA),32)'], textCDL:['Equal(MeasureOfAngle(OBA),32)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(BA,O)'... | 4839 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=8, the radius of circle O is 3, O is the center of circle O, C bisects segment AB, the tangent to ⊙O is AC, the tangent to ⊙O is BC. Find the length of line OA. Please provide the consCDL and imgCDL based on this given geometric diagram and pro... | consCDL:['Shape(CA,AM,OCM)', 'Shape(OCM,MO,OC)', 'Shape(BC,ONC,NB)', 'Shape(ONC,CO,ON)', 'Shape(OM,OMN,NO)', 'Collinear(ACB)', 'Collinear(AMO)', 'Collinear(BNO)', 'Cocircular(O,NCM)'], imgCDL:['Equal(LengthOfLine(AB),8)'], textCDL:['Equal(LengthOfLine(AB),8)', 'Equal(RadiusOfCircle(O),3)', 'IsCentreOfCircle(O,O)', 'IsM... | 4843 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠OAB=20°, O is the center of ⊙O, the tangent to ⊙O is AB. Find the measure of ∠ODC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> ta... | consCDL:['Shape(DO,OB,OBD)', 'Shape(OD,DC,CO)', 'Shape(CD,ODC)', 'Shape(BO,OE,OEB)', 'Shape(EO,OC,OCE)', 'Shape(EA,AB,OEB)', 'Collinear(DOEA)', 'Collinear(BOC)', 'Cocircular(O,BDCE)'], imgCDL:['Equal(MeasureOfAngle(OAB),20)'], textCDL:['Equal(MeasureOfAngle(OAB),20)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(AB,O)']... | 4871 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, PA=5, ∠PAQ=120°, O is the center of circle O, the tangent to circle O is AP, the tangent to circle O is AQ. Find the radius of circle O. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on i... | consCDL:['Shape(PO,OQ,OQP)', 'Shape(DO,OP,OPD)', 'Shape(PA,AD,OPD)', 'Shape(QO,OD,ODQ)', 'Shape(DA,AQ,ODQ)', 'Collinear(ODA)', 'Cocircular(O,PDQ)'], imgCDL:['Equal(LengthOfLine(PA),5)', 'Equal(MeasureOfAngle(PAQ),120)'], textCDL:['Equal(LengthOfLine(PA),5)', 'Equal(MeasureOfAngle(PAQ),120)', 'IsCentreOfCircle(O,O)', 'I... | 4888 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, Radius(⊙O) is 2, O is the center of ⊙O. Find the area of the ⊙O. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide... | consCDL:['Shape(O)', 'Cocircular(O)'], imgCDL:[], textCDL:['Equal(RadiusOfCircle(O),2)', 'IsCentreOfCircle(O,O)']. | 4915 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=3, BC=4, BM=1, MN is perpendicular to DN, quadrilateral ADCB is a rectangle. Find the length of line DN. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think w... | consCDL:['Shape(AN,NM,MB,BA)', 'Shape(AD,DN,NA)', 'Shape(ND,DC,CM,MN)', 'Collinear(ANM)', 'Collinear(BMC)'], imgCDL:['Equal(LengthOfLine(AB),3)', 'Equal(LengthOfLine(BC),4)', 'Equal(LengthOfLine(BM),1)', 'PerpendicularBetweenLine(MN,DN)'], textCDL:['Equal(LengthOfLine(AB),3)', 'Equal(LengthOfLine(BC),4)', 'Equal(Length... | 4928 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AF=4, BD=CD, ED=2AE, BF is parallel to DG. Find the length of line AC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then p... | consCDL:['Shape(EB,BD,DE)', 'Shape(ED,DG,GF,FE)', 'Shape(DC,CG,GD)', 'Shape(AE,EF,FA)', 'Collinear(AED)', 'Collinear(AFGC)', 'Collinear(BEF)', 'Collinear(BDC)'], imgCDL:['Equal(LengthOfLine(AF),4)', 'Equal(LengthOfLine(BD),LengthOfLine(CD))', 'ParallelBetweenLine(BF,DG)'], textCDL:['Equal(LengthOfLine(AF),4)', 'Equal(L... | 4966 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AE=4, BF=3, Triangle AED is mirror similar to triangle BFA., quadrilateral ABCD is a square. Find the area of quadrilateral ABCD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its capt... | consCDL:['Shape(AB,BF,FA)', 'Shape(AF,FE,ED,DA)', 'Shape(FB,BC,CE,EF)', 'Collinear(AFE)', 'Collinear(DEC)'], imgCDL:['Equal(LengthOfLine(AE),4)', 'Equal(LengthOfLine(BF),3)'], textCDL:['Equal(LengthOfLine(AE),4)', 'Equal(LengthOfLine(BF),3)', 'MirrorSimilarBetweenTriangle(AED,BFA)', 'Square(ABCD)']. | 5062 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CEM=80°, ∠MFC=50°, AB is parallel to CF, CE∥AD. Find ∠BAD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all ... | consCDL:['Shape(AC,CB,BA)', 'Shape(AD,DC,CA)', 'Shape(CE,EM,MC)', 'Shape(CM,MF,FC)', 'Shape(BC,CF)', 'Shape(DC,CE)', 'Collinear(ACM)', 'Collinear(EMF)'], imgCDL:['Equal(MeasureOfAngle(CEM),80)', 'Equal(MeasureOfAngle(MFC),50)', 'ParallelBetweenLine(AB,CF)', 'ParallelBetweenLine(CE,AD)'], textCDL:['Equal(MeasureOfAngle(... | 5108 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=10, AC=16, AI is the angle bisector of ∠CAD, M bisects segment BC, AC is parallel to IM. Find the length of line MI. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You f... | consCDL:['Shape(AD,DI,IA)', 'Shape(AI,IM,MC,CA)', 'Shape(BM,MI,ID,DB)', 'Collinear(DIM)', 'Collinear(BMC)', 'Collinear(ADB)'], imgCDL:['Equal(LengthOfLine(AB),10)', 'Equal(LengthOfLine(AC),16)', 'ParallelBetweenLine(AC,IM)'], textCDL:['Equal(LengthOfLine(AB),10)', 'Equal(LengthOfLine(AC),16)', 'IsBisectorOfAngle(AI,CAD... | 5119 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAD=20°, AD is the angle bisector of ∠CAB, AE bisects ∠FAC. Find ∠EAC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then ... | consCDL:['Shape(FA,AE)', 'Shape(EA,AC)', 'Shape(AB,BD,DA)', 'Shape(AD,DC,CA)', 'Shape(AC,CG)', 'Collinear(FAB)', 'Collinear(BDCG)'], imgCDL:['Equal(MeasureOfAngle(CAD),20)'], textCDL:['Equal(MeasureOfAngle(CAD),20)', 'IsBisectorOfAngle(AD,CAB)', 'IsBisectorOfAngle(AE,FAC)']. | 5149 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=4, ∠COP=60°, O is the center of circle O, D is the midpoint of ⌒OBC, PF⊥DF. Find the sum of the length of line CP and the length of line PD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL bas... | consCDL:['Shape(OAE,EO,OA)', 'Shape(OE,EP,PO)', 'Shape(PE,EF,FP)', 'Shape(OEB,BF,FE)', 'Shape(OBD,DF,FB)', 'Shape(DP,PF,FD)', 'Shape(ODC,CP,PD)', 'Shape(CO,OP,PC)', 'Shape(OCA,AO,OC)', 'Collinear(AOPFB)', 'Collinear(DFE)', 'Collinear(CPE)', 'Cocircular(O,AEBDC)'], imgCDL:['Equal(LengthOfLine(AB),4)', 'Equal(MeasureOfAn... | 5206 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DPB=20°, ∠EAB=50°, BP bisects ∠ABC, DP is the angle bisector of ∠ADC. Find the measure of ∠BCD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <thin... | consCDL:['Shape(AB,BE,EA)', 'Shape(AE,EP,PA)', 'Shape(PE,ED,DP)', 'Shape(PD,DC,CP)', 'Shape(EB,BM,MD,DE)', 'Shape(DM,MC,CD)', 'Collinear(AED)', 'Collinear(BEP)', 'Collinear(PDM)', 'Collinear(BMC)'], imgCDL:['Equal(MeasureOfAngle(DPB),20)', 'Equal(MeasureOfAngle(EAB),50)'], textCDL:['Equal(MeasureOfAngle(DPB),20)', 'Equ... | 5236 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AQF=100°, ∠BPA=126°. Find the measure of ∠DAP minus the measure of ∠QFD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and the... | consCDL:['Shape(AB,BP,PA)', 'Shape(PB,BC,CP)', 'Shape(AP,PD,DA)', 'Shape(PC,CQ,QD,DP)', 'Shape(AD,DF,FA)', 'Shape(DQ,QF,FD)', 'Collinear(BPDF)', 'Collinear(APC)', 'Collinear(ADQ)', 'Collinear(BCQ)'], imgCDL:['Equal(MeasureOfAngle(AQF),100)', 'Equal(MeasureOfAngle(BPA),126)'], textCDL:['Equal(MeasureOfAngle(AQF),100)', ... | 5262 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=3, the ratio of similar triangles ACB and DFE is 2/3, △ACB is similar to △DFE.. Find DE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></t... | consCDL:['Shape(AO,OC,CA)', 'Shape(AC,CM,MA)', 'Shape(DA,AM,MF,FD)', 'Shape(DF,FE,ED)', 'Shape(CO,OB,BC)', 'Shape(CB,BM,MC)', 'Shape(FM,MB,BE,EF)', 'Collinear(OAD)', 'Collinear(OCMF)', 'Collinear(OBE)', 'Collinear(AMB)'], imgCDL:['Equal(LengthOfLine(AB),3)'], textCDL:['Equal(LengthOfLine(AB),3)', 'Equal(RatioOfSimilarT... | 5342 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BD=1/5, Radius(⊙O) is 1, O is the center of ⊙O, AB⊥OB. Find AC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide ... | consCDL:['Shape(OA,AB,BO)', 'Shape(OB,BC,CO)', 'Shape(BA,OAD,DB)', 'Shape(CB,BD,ODC)', 'Shape(OC,OCA,AO)', 'Collinear(ABC)', 'Collinear(OBD)', 'Cocircular(O,ADC)'], imgCDL:['Equal(LengthOfLine(BD),1/5)', 'PerpendicularBetweenLine(AB,OB)'], textCDL:['Equal(LengthOfLine(BD),1/5)', 'Equal(RadiusOfCircle(O),1)', 'IsCentreO... | 5353 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=13, AB=AC, AE=ED, BC=10, AD is the angle bisector of ∠BAC. Find Perimeter(△DEC). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> ta... | consCDL:['Shape(AD,DC,CA)', 'Shape(AE,ED,DA)', 'Shape(DE,EB,BD)', 'Collinear(AEB)', 'Collinear(CDB)'], imgCDL:['Equal(LengthOfLine(AB),13)', 'Equal(LengthOfLine(AB),LengthOfLine(AC))', 'Equal(LengthOfLine(AE),LengthOfLine(ED))', 'Equal(LengthOfLine(BC),10)'], textCDL:['Equal(LengthOfLine(AB),13)', 'Equal(LengthOfLine(A... | 5406 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=7, AD=4, AF bisects ∠DAB, BA and CD are opposite sides of the ▱ ABCD. Find the length of line CF. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <... | consCDL:['Shape(ED,DA,AE)', 'Shape(AB,BC,CE,EA)', 'Shape(FE,EC,CF)', 'Collinear(DEC)', 'Collinear(AEF)', 'Collinear(BCF)'], imgCDL:['Equal(LengthOfLine(AB),7)', 'Equal(LengthOfLine(AD),4)'], textCDL:['Equal(LengthOfLine(AB),7)', 'Equal(LengthOfLine(AD),4)', 'IsBisectorOfAngle(AF,DAB)', 'Parallelogram(ABCD)']. | 5422 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ED=6, FG=2, BG is the angle bisector of ∠ABC, CF bisects ∠BCA, EG∥BC, FD is parallel to BC. Find the sum of EB and DC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You fi... | consCDL:['Shape(AE,EF,FG,GD,DA)', 'Shape(EB,BH,HF,FE)', 'Shape(GF,FH,HG)', 'Shape(DG,GH,HC,CD)', 'Shape(HB,BC,CH)', 'Collinear(EFGD)', 'Collinear(FHC)', 'Collinear(GHB)', 'Collinear(AEB)', 'Collinear(ADC)'], imgCDL:['Equal(LengthOfLine(ED),6)', 'Equal(LengthOfLine(FG),2)', 'ParallelBetweenLine(EG,BC)', 'ParallelBetween... | 5438 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, CD=36, ∠ACB=30°, triangle BAC is mirror congruent to triangle DCA, BA is perpendicular to CA. Find the length of line BA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You... | consCDL:['Shape(BA,AC,CB)', 'Shape(AD,DC,CA)', 'Shape(BA,AD)'], imgCDL:['Equal(LengthOfLine(CD),36)', 'Equal(MeasureOfAngle(ACB),30)', 'PerpendicularBetweenLine(BA,CA)'], textCDL:['Equal(LengthOfLine(CD),36)', 'Equal(MeasureOfAngle(ACB),30)', 'MirrorCongruentBetweenTriangle(BAC,DCA)', 'PerpendicularBetweenLine(BA,CA)']... | 5471 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AE=12, BF=8, D bisects segment AB, P bisects segment AF, Q is the midpoint of segment EB, BC and CA are the legs of the right triangle BCA. Find the length of line PQ. Please provide the consCDL and imgCDL based on this given geometric diagram and... | consCDL:['Shape(CA,AP,PF,FC)', 'Shape(AG,GP,PA)', 'Shape(PG,GD,DP)', 'Shape(PD,DB,BF,FP)', 'Shape(AE,EQ,QG,GA)', 'Shape(DG,GQ,QD)', 'Shape(BD,DQ,QB)', 'Collinear(EQB)', 'Collinear(AGDB)', 'Collinear(APF)', 'Collinear(EAC)', 'Collinear(BFC)', 'Collinear(PGQ)'], imgCDL:['Equal(LengthOfLine(AE),12)', 'Equal(LengthOfLine(B... | 5492 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AD=BC, ∠BCA=87°, ∠DAC=15°, E bisects segment AB, F is the midpoint of segment CD, G bisects segment AC. Find the measure of ∠GEF. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its capt... | consCDL:['Shape(DA,AG,GF,FD)', 'Shape(FG,GH,HF)', 'Shape(CF,FH,HC)', 'Shape(AE,EG,GA)', 'Shape(HG,GE,EH)', 'Shape(CH,HE,EB,BC)', 'Collinear(DFC)', 'Collinear(AGHC)', 'Collinear(AEB)', 'Collinear(FHE)'], imgCDL:['Equal(LengthOfLine(AD),LengthOfLine(BC))', 'Equal(MeasureOfAngle(BCA),87)', 'Equal(MeasureOfAngle(DAC),15)']... | 5507 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=4, ∠BCA=60°, C is the center of ⊙C, AD is perpendicular to CD. Find Area(CAB). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags... | consCDL:['Shape(CA,AD,DC)', 'Shape(AD,DB,BA)', 'Shape(BA,CAB)', 'Shape(AC,CD,DB,CBA)', 'Collinear(CDB)', 'Cocircular(C,AB)'], imgCDL:['Equal(LengthOfLine(AB),4)', 'Equal(MeasureOfAngle(BCA),60)', 'PerpendicularBetweenLine(AD,CD)'], textCDL:['Equal(LengthOfLine(AB),4)', 'Equal(MeasureOfAngle(BCA),60)', 'IsCentreOfCircle... | 5526 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BD=6, ∠BDO=90°, ∠OBD=30°, triangle ABC is an equilateral triangle, O is the center of ⊙O, the incenter of triangle ABC is O. Find the area of the sector OED. Please provide the consCDL and imgCDL based on this given geometric diagram and provide t... | consCDL:['Shape(OE,OED,DO)', 'Shape(OD,ODF,OFG,OGE,EO)', 'Shape(DC,CF,ODF)', 'Shape(FA,AG,OFG)', 'Shape(BE,OGE,GB)', 'Shape(EB,BD,OED)', 'Collinear(AGB)', 'Collinear(AFC)', 'Collinear(BDC)', 'Collinear(BEO)', 'Cocircular(O,FGED)'], imgCDL:['Equal(LengthOfLine(BD),6)', 'Equal(MeasureOfAngle(BDO),90)', 'Equal(MeasureOfAn... | 5529 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=BD, AC=6, EC=1, the center of ⊙O is O, AC is the diameter of ⊙O, OB is parallel to DC. Find AD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <th... | consCDL:['Shape(AB,OBA)', 'Shape(DA,OAD)', 'Shape(CD,ODC)', 'Shape(AD,DE,EO,OA)', 'Shape(ED,DC,CE)', 'Shape(BA,AO,OB)', 'Shape(BO,OE,EB)', 'Shape(BE,EC,OCB)', 'Collinear(AOEC)', 'Collinear(BED)', 'Cocircular(O,ADCB)'], imgCDL:['Equal(LengthOfLine(AB),LengthOfLine(BD))', 'Equal(LengthOfLine(AC),6)', 'Equal(LengthOfLine(... | 5827 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, DE/EA=2/3, CD=10, EF∥AB, quadrilateral DABC is a parallelogram. Find EF. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then... | consCDL:['Shape(DE,EF,FD)', 'Shape(FE,EA,AB,BF)', 'Shape(CD,DF,FB,BC)', 'Collinear(DEA)', 'Collinear(DFB)'], imgCDL:['Equal(LengthOfLine(CD),10)', 'ParallelBetweenLine(EF,AB)'], textCDL:['Equal(Div(LengthOfLine(DE),LengthOfLine(EA)),2/3)', 'Equal(LengthOfLine(CD),10)', 'ParallelBetweenLine(EF,AB)', 'Parallelogram(DABC)... | 5889 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, CD=20, DE=10, ∠BCA=60°, ∠BDF=30°, CA⊥FA, DE is perpendicular to CE, GF is perpendicular to BF. Find AB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think withi... | consCDL:['Shape(CD,DE,EC)', 'Shape(GD,DC,CG)', 'Shape(FG,GC,CA,AF)', 'Shape(BD,DG,GB)', 'Shape(BG,GF,FB)', 'Collinear(DGF)', 'Collinear(ECA)', 'Collinear(BGC)', 'Collinear(BFA)'], imgCDL:['Equal(LengthOfLine(CD),20)', 'Equal(LengthOfLine(DE),10)', 'Equal(MeasureOfAngle(BCA),60)', 'Equal(MeasureOfAngle(BDF),30)', 'Perpe... | 5929 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, Radius(⊙O) is 2, the center of circle O is O, PA is the tangent to circle O, the tangent to ⊙O is PB, BP is perpendicular to AP. Find the length of line OP. Please provide the consCDL and imgCDL based on this given geometric diagram and provide th... | consCDL:['Shape(CP,PA,OCA)', 'Shape(BP,PC,OBC)', 'Shape(AO,OC,OCA)', 'Shape(CO,OB,OBC)', 'Shape(OA,OAB,BO)', 'Collinear(PCO)', 'Cocircular(O,ABC)'], imgCDL:['PerpendicularBetweenLine(BP,AP)'], textCDL:['Equal(RadiusOfCircle(O),2)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(PA,O)', 'IsTangentOfCircle(PB,O)', 'Perpendi... | 5966 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=AC, BF=8, CB=10, triangle DBF is an equilateral triangle, AH is the altitude of △ ABC. Find DE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <th... | consCDL:['Shape(AB,BD,DE,EA)', 'Shape(AE,EF,FC,CA)', 'Shape(DB,BH,HE,ED)', 'Shape(EH,HF,FE)', 'Collinear(AEH)', 'Collinear(DEF)', 'Collinear(BHFC)'], imgCDL:['Equal(LengthOfLine(AB),LengthOfLine(AC))', 'Equal(LengthOfLine(BF),8)', 'Equal(LengthOfLine(CB),10)'], textCDL:['Equal(LengthOfLine(AB),LengthOfLine(AC))', 'Equa... | 5974 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠OAB=22°, O is the center of ⊙O. Find the measure of ∠ACB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all C... | consCDL:['Shape(DA,AO,OB,BD)', 'Shape(OA,AB,BO)', 'Shape(BA,AC,CB)', 'Shape(DB,OBD)', 'Shape(AD,ODA)', 'Shape(CA,OAC)', 'Shape(BC,OCB)', 'Cocircular(O,ACBD)'], imgCDL:['Equal(MeasureOfAngle(OAB),22)'], textCDL:['Equal(MeasureOfAngle(OAB),22)', 'IsCentreOfCircle(O,O)']. | 6003 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CBO=70°, O is the center of ⊙O. Find the measure of ∠BAC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all C... | consCDL:['Shape(AD,DB,BA)', 'Shape(BD,DC,CB)', 'Shape(OAC,CO,OD,DA)', 'Shape(OCB,BC)', 'Shape(OBA,AB)', 'Shape(CD,DO,OC)', 'Collinear(ADC)', 'Collinear(BDO)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(CBO),70)'], textCDL:['Equal(MeasureOfAngle(CBO),70)', 'IsCentreOfCircle(O,O)']. | 6042 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BAC=15°, the center of ⊙O is O. Find the measure of ∠CBO. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all C... | consCDL:['Shape(CO,OD,DA,OAC)', 'Shape(DO,OC,CD)', 'Shape(DC,CB,BD)', 'Shape(BC,OCB)', 'Shape(AD,DB,BA)', 'Shape(AB,OBA)', 'Collinear(ADC)', 'Collinear(ODB)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(BAC),15)'], textCDL:['Equal(MeasureOfAngle(BAC),15)', 'IsCentreOfCircle(O,O)']. | 6113 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CDA=52°, the center of circle O is O, AD and BC are opposite sides of the parallelogram ABCD. Find the measure of ∠BEA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You ... | consCDL:['Shape(BA,OAB)', 'Shape(AB,BO,OC,CF,FA)', 'Shape(AF,FD,DA)', 'Shape(AD,ODA)', 'Shape(DF,FE,OED)', 'Shape(FC,CE,EF)', 'Shape(EC,CO,OB,OBE)', 'Collinear(AFE)', 'Collinear(DFC)', 'Collinear(BOCE)', 'Cocircular(O,ABED)'], imgCDL:['Equal(MeasureOfAngle(CDA),52)'], textCDL:['Equal(MeasureOfAngle(CDA),52)', 'IsCentre... | 6150 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BDE=15°, ∠ECA=25°, the center of circle O is O. Find ∠BOA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all ... | consCDL:['Shape(AC,OCA)', 'Shape(CA,AF,FC)', 'Shape(CF,FO,OG,GD,ODC)', 'Shape(DG,GB,BD)', 'Shape(DB,OBD)', 'Shape(BG,GE,OEB)', 'Shape(EG,GO,OF,FE)', 'Shape(EF,FA,OAE)', 'Collinear(CFE)', 'Collinear(AFO)', 'Collinear(DGE)', 'Collinear(OGB)', 'Cocircular(O,CAEBD)'], imgCDL:['Equal(MeasureOfAngle(BDE),15)', 'Equal(Measure... | 6190 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BDC=20°, ∠DOA=110°, the center of ⊙O is O. Find the measure of ∠CPB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then pr... | consCDL:['Shape(CP,PB,OCB)', 'Shape(BD,DC,OCB)', 'Shape(DB,BA,AO,OD)', 'Shape(CD,ODC)', 'Shape(AB,OBA)', 'Shape(DO,OA,OAD)', 'Collinear(PBA)', 'Collinear(PCD)', 'Cocircular(O,CBAD)'], imgCDL:['Equal(MeasureOfAngle(BDC),20)', 'Equal(MeasureOfAngle(DOA),110)'], textCDL:['Equal(MeasureOfAngle(BDC),20)', 'Equal(MeasureOfAn... | 6208 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=10, CD=6, O is the center of circle O, the center of ⊙P is O, P is the center of circle P, CE is perpendicular to OE. Find the length of line AC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCD... | consCDL:['Shape(OCD,DE,EC)', 'Shape(ODC,CO,OE,ED)', 'Shape(PAB,BD,OCD,CA)', 'Shape(PBA,AC,ODC,DB)', 'Shape(OC,CE,EO)', 'Collinear(ACEDB)', 'Cocircular(P,AB)', 'Cocircular(O,CD)'], imgCDL:['Equal(LengthOfLine(AB),10)', 'Equal(LengthOfLine(CD),6)', 'PerpendicularBetweenLine(CE,OE)'], textCDL:['Equal(LengthOfLine(AB),10)'... | 6245 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=4, BC=6, DE=2, O is the center of circle O, CM⊥OM, quadrilateral ADHG is a rectangle. Find the length of line DF. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You firs... | consCDL:['Shape(OCB,BM,MC)', 'Shape(OF,OFC,CM,MO)', 'Shape(OM,MB,OBE,EO)', 'Shape(OEF,FO,OE)', 'Shape(AD,DE,OBE,BA)', 'Shape(OFC,FH,HG,GC)', 'Collinear(ABMCG)', 'Collinear(DEOFH)', 'Cocircular(O,CBEF)'], imgCDL:['Equal(LengthOfLine(AB),4)', 'Equal(LengthOfLine(BC),6)', 'Equal(LengthOfLine(DE),2)', 'PerpendicularBetween... | 6253 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABO=70°, O is the center of ⊙O, CA is the tangent to ⊙O. Find ∠BAC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then pro... | consCDL:['Shape(BO,OA,AB)', 'Shape(OAB,BA)', 'Shape(OB,OBA,AO)', 'Shape(AC)', 'Cocircular(O,AB)'], imgCDL:['Equal(MeasureOfAngle(ABO),70)'], textCDL:['Equal(MeasureOfAngle(ABO),70)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(CA,O)']. | 6285 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DAB=110°, FE perpendicular bisects AB, quadrilateral ABCD is a rhombus. Find ∠CDF. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> ta... | consCDL:['Shape(AE,EF,FA)', 'Shape(EB,BC,CF,FE)', 'Shape(AF,FD,DA)', 'Shape(FC,CD,DF)', 'Collinear(AEB)', 'Collinear(AFC)'], imgCDL:['Equal(MeasureOfAngle(DAB),110)'], textCDL:['Equal(MeasureOfAngle(DAB),110)', 'IsPerpendicularBisectorOfLine(FE,AB)', 'Rhombus(ABCD)']. | 6359 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BCE=42°, BA and CD are opposite sides of the ▱ ABCD, CE is perpendicular to BE. Find the measure of ∠CDA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think wi... | consCDL:['Shape(EA,AF,FE)', 'Shape(AB,BC,CF,FA)', 'Shape(FC,CD,DF)', 'Shape(EF,FD)', 'Collinear(AFD)', 'Collinear(EFC)', 'Collinear(BAE)'], imgCDL:['Equal(MeasureOfAngle(BCE),42)', 'PerpendicularBetweenLine(CE,BE)'], textCDL:['Equal(MeasureOfAngle(BCE),42)', 'Parallelogram(ABCD)', 'PerpendicularBetweenLine(CE,BE)']. | 6372 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=3, BC=5, CF=2, BE is the angle bisector of ∠ABC, CF bisects ∠BCD, FC∥AM, quadrilateral ABCD is a parallelogram. Find BE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. Y... | consCDL:['Shape(AB,BO,OA)', 'Shape(AO,OG,GF,FA)', 'Shape(FG,GE,EF)', 'Shape(GO,OM,MC,CG)', 'Shape(BM,MO,OB)', 'Shape(EG,GC,CD,DE)', 'Collinear(AFED)', 'Collinear(BOGE)', 'Collinear(FGC)', 'Collinear(AOM)', 'Collinear(BMC)'], imgCDL:['Equal(LengthOfLine(AB),3)', 'Equal(LengthOfLine(BC),5)', 'Equal(LengthOfLine(CF),2)', ... | 6378 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=10, DG=3, AE is the angle bisector of ∠DAB, F is the midpoint of segment CD, AD and BC are opposite sides of the ▱ ABCD, DG⊥FG. Find the length of line AE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide ... | consCDL:['Shape(AG,GD,DA)', 'Shape(DG,GF,FD)', 'Shape(FC,CE,EF)', 'Shape(AB,BC,CF,FG,GA)', 'Shape(DF,FE)', 'Collinear(AGFE)', 'Collinear(DFC)', 'Collinear(BCE)'], imgCDL:['Equal(LengthOfLine(AB),10)', 'Equal(LengthOfLine(DG),3)', 'PerpendicularBetweenLine(DG,FG)'], textCDL:['Equal(LengthOfLine(AB),10)', 'Equal(LengthOf... | 6406 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=6, AD=9, ∠DAB=120°, AE bisects ∠DAB, quadrilateral ABCD is a ▱. Find the perimeter of △EFC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think>... | consCDL:['Shape(AB,BE,EA)', 'Shape(AE,EC,CD,DA)', 'Shape(EF,FC,CE)', 'Shape(BE,EF)', 'Collinear(BEC)', 'Collinear(DCF)', 'Collinear(AEF)'], imgCDL:['Equal(LengthOfLine(AB),6)', 'Equal(LengthOfLine(AD),9)', 'Equal(MeasureOfAngle(DAB),120)'], textCDL:['Equal(LengthOfLine(AB),6)', 'Equal(LengthOfLine(AD),9)', 'Equal(Measu... | 6420 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, Perimeter(ABCD) is 16, quadrilateral ABCD is a ▱, AO⊥EO. Find Perimeter(△DEC). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags an... | consCDL:['Shape(AO,OE,EA)', 'Shape(EO,OF,FE)', 'Shape(EF,FD,DE)', 'Shape(FO,OC,CF)', 'Shape(FC,CD,DF)', 'Shape(AB,BO,OA)', 'Shape(OB,BC,CO)', 'Collinear(AOC)', 'Collinear(BOFD)', 'Collinear(AED)', 'Collinear(EFC)'], imgCDL:['PerpendicularBetweenLine(AO,EO)'], textCDL:['Equal(PerimeterOfQuadrilateral(ABCD),16)', 'Parall... | 6497 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=3, AD=5, EO is the perpendicular bisector of BD, ADCB is a ▱. Find the perimeter of triangle CED. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <... | consCDL:['Shape(BA,AF,FO,OB)', 'Shape(BO,OE,EB)', 'Shape(EO,OD,DE)', 'Shape(CE,ED,DC)', 'Shape(OF,FD,DO)', 'Collinear(BEC)', 'Collinear(AFD)', 'Collinear(BOD)', 'Collinear(EOF)'], imgCDL:['Equal(LengthOfLine(AB),3)', 'Equal(LengthOfLine(AD),5)'], textCDL:['Equal(LengthOfLine(AB),3)', 'Equal(LengthOfLine(AD),5)', 'IsPer... | 6532 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABC=80°, AE bisects ∠DAB, EA∥CF, quadrilateral ABCD is a ▱. Find the measure of ∠ECF. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think>... | consCDL:['Shape(AB,BE,EA)', 'Shape(AE,EC,CF,FA)', 'Shape(FC,CD,DF)', 'Collinear(AFD)', 'Collinear(BEC)'], imgCDL:['Equal(MeasureOfAngle(ABC),80)', 'ParallelBetweenLine(EA,CF)'], textCDL:['Equal(MeasureOfAngle(ABC),80)', 'IsBisectorOfAngle(AE,DAB)', 'ParallelBetweenLine(EA,CF)', 'Parallelogram(ABCD)']. | 6541 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, the perimeter of triangle ABE is 12, ABCD is a ▱, EO is perpendicular to DO. Find the perimeter of ABCD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think with... | consCDL:['Shape(AB,BF,FA)', 'Shape(AF,FE,EA)', 'Shape(EF,FO,OE)', 'Shape(FB,BO,OF)', 'Shape(OB,BC,CO)', 'Shape(EO,OD,DE)', 'Shape(DO,OC,CD)', 'Collinear(AFOC)', 'Collinear(BFE)', 'Collinear(AED)', 'Collinear(BOD)'], imgCDL:['PerpendicularBetweenLine(EO,DO)'], textCDL:['Equal(PerimeterOfTriangle(ABE),12)', 'Parallelogra... | 6573 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CBO=52°, ⌒OAD=⌒ODC, the center of ⊙O is O, AB is the diameter of ⊙O. Find the measure of ∠BAD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think... | consCDL:['Shape(BC,OCB)', 'Shape(CD,ODC)', 'Shape(DA,OAD)', 'Shape(AO,OB,OBA)', 'Shape(CB,BD,DC)', 'Shape(DB,BO,OA,AD)', 'Collinear(BOA)', 'Cocircular(O,ADCB)'], imgCDL:['Equal(MeasureOfAngle(CBO),52)', 'Equal(MeasureOfArc(OAD),MeasureOfArc(ODC))'], textCDL:['Equal(MeasureOfAngle(CBO),52)', 'Equal(MeasureOfArc(OAD),Mea... | 6607 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, Diameter(⊙O) is 6, ∠BAE=60°, O is the center of ⊙O, BD is the diameter of ⊙O. Find the length of line BC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think wit... | consCDL:['Shape(AB,OBA)', 'Shape(DE,EA,OAD)', 'Shape(CD,ODC)', 'Shape(BC,OCB)', 'Shape(BA,AE,EO,OB)', 'Shape(BO,OE,EC,CB)', 'Shape(CE,ED,DC)', 'Collinear(BOED)', 'Collinear(AEC)', 'Cocircular(O,ADCB)'], imgCDL:['Equal(MeasureOfAngle(BAE),60)'], textCDL:['Equal(DiameterOfCircle(O),6)', 'Equal(MeasureOfAngle(BAE),60)', '... | 6619 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAO=20°, ∠CBO=50°, O is the center of circle O. Find the measure of ∠AOB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and th... | consCDL:['Shape(OA,OAC,CM,MO)', 'Shape(AO,OM,MA)', 'Shape(MC,CB,BM)', 'Shape(AM,MB,BA)', 'Shape(OBA,AB)', 'Shape(OCB,BC)', 'Collinear(AMC)', 'Collinear(OMB)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(CAO),20)', 'Equal(MeasureOfAngle(CBO),50)'], textCDL:['Equal(MeasureOfAngle(CAO),20)', 'Equal(MeasureOfAngle(... | 6663 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BAC=40°, O is the center of circle O. Find ∠BOC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs withi... | consCDL:['Shape(BO,OC,CB)', 'Shape(BC,OCB)', 'Shape(OB,BA,AC,CO)', 'Shape(AB,OBA)', 'Shape(CA,OAC)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(BAC),40)'], textCDL:['Equal(MeasureOfAngle(BAC),40)', 'IsCentreOfCircle(O,O)']. | 6713 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DAB=60°, O is the center of circle O, AB is the diameter of circle O, AD∥OC. Find ∠DAC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></thin... | consCDL:['Shape(AD,ODA)', 'Shape(DA,AC,OCD)', 'Shape(CO,OB,OBC)', 'Shape(AO,OC,CA)', 'Shape(BO,OA,OAB)', 'Collinear(AOB)', 'Cocircular(O,ABCD)'], imgCDL:['Equal(MeasureOfAngle(DAB),60)', 'ParallelBetweenLine(AD,OC)'], textCDL:['Equal(MeasureOfAngle(DAB),60)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)', 'Parall... | 6726 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAB=25°, ∠DEC=30°, the center of circle O is O. Find ∠DOB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all ... | consCDL:['Shape(BA,OAB)', 'Shape(AB,BF,FA)', 'Shape(AF,FE,OEA)', 'Shape(FB,BM,MF)', 'Shape(CM,MB,OBC)', 'Shape(OM,MC,CN,NO)', 'Shape(DN,NC,OCD)', 'Shape(EN,ND,DE)', 'Shape(ED,ODE)', 'Shape(EF,FM,MO,ON,NE)', 'Collinear(AFMC)', 'Collinear(BMO)', 'Collinear(DNO)', 'Collinear(ENC)', 'Collinear(BFE)', 'Cocircular(O,ABCDE)']... | 6731 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BAP=40°, O is the center of ⊙O, AP is the tangent to circle O. Find the measure of ∠APB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></thi... | consCDL:['Shape(BA,AP,OBP)', 'Shape(OBP,PO,OB)', 'Shape(BO,OP,OPB)', 'Collinear(OBA)', 'Cocircular(O,BP)'], imgCDL:['Equal(MeasureOfAngle(BAP),40)'], textCDL:['Equal(MeasureOfAngle(BAP),40)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(AP,O)']. | 6783 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BOC=76°, O is the center of ⊙O, EC is the tangent to ⊙O. Find ∠BCE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then pro... | consCDL:['Shape(AC,CO,OB,BA)', 'Shape(OC,CB,BO)', 'Shape(BC,OCB)', 'Shape(CE)', 'Shape(AB,OBA)', 'Shape(CA,OAC)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(BOC),76)'], textCDL:['Equal(MeasureOfAngle(BOC),76)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(EC,O)']. | 6788 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABO=65°, the center of circle O is O, the tangent to ⊙O is CA. Find the measure of ∠BAC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></thi... | consCDL:['Shape(AO,OB,OBA)', 'Shape(OA,AB,BO)', 'Shape(BA,OAB)', 'Shape(AC)', 'Cocircular(O,AB)'], imgCDL:['Equal(MeasureOfAngle(ABO),65)'], textCDL:['Equal(MeasureOfAngle(ABO),65)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(CA,O)']. | 6791 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BD=BC, ∠BCD=55°, ABCD is a ▱, BE⊥AE. Find the measure of ∠EAB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide a... | consCDL:['Shape(DA,AE,ED)', 'Shape(EA,AB,BE)', 'Shape(CD,DE,EB,BC)', 'Collinear(DEB)'], imgCDL:['Equal(LengthOfLine(BD),LengthOfLine(BC))', 'Equal(MeasureOfAngle(BCD),55)', 'PerpendicularBetweenLine(BE,AE)'], textCDL:['Equal(LengthOfLine(BD),LengthOfLine(BC))', 'Equal(MeasureOfAngle(BCD),55)', 'Parallelogram(ABCD)', 'P... | 6818 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DAE=20°, ∠ECD=35°, ∠FBE=45°. Find ∠DFE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></... | consCDL:['Shape(AF,FD,DA)', 'Shape(FB,BE,EF)', 'Shape(DF,FE,EC,CD)', 'Shape(AF,FB)', 'Collinear(AFE)', 'Collinear(ADC)', 'Collinear(DFB)', 'Collinear(BEC)'], imgCDL:['Equal(MeasureOfAngle(DAE),20)', 'Equal(MeasureOfAngle(ECD),35)', 'Equal(MeasureOfAngle(FBE),45)'], textCDL:['Equal(MeasureOfAngle(DAE),20)', 'Equal(Measu... | 6847 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AD=CD, ∠FEB=70°, the center of circle O is O, the diameter of circle O is AB. Find ∠ABC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></thin... | consCDL:['Shape(AD,ODA)', 'Shape(DA,AF,FD)', 'Shape(DC,OCD)', 'Shape(DF,FO,OD)', 'Shape(DO,OB,BD)', 'Shape(CD,DB,BC)', 'Shape(CB,OBC)', 'Shape(BE,OEB)', 'Shape(BO,OF,FE,EB)', 'Shape(EF,FA,OAE)', 'Collinear(AFOB)', 'Collinear(DFE)', 'Cocircular(O,DAEBC)'], imgCDL:['Equal(LengthOfLine(AD),LengthOfLine(CD))', 'Equal(Measu... | 6862 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠OBA=40°, the center of circle O is O. Find ∠ACB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs withi... | consCDL:['Shape(AO,OD,DA)', 'Shape(AD,DB,BA)', 'Shape(AB,OBA)', 'Shape(BD,DC,CB)', 'Shape(BC,OCB)', 'Shape(CD,DO,OA,OAC)', 'Collinear(ADC)', 'Collinear(ODB)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(OBA),40)'], textCDL:['Equal(MeasureOfAngle(OBA),40)', 'IsCentreOfCircle(O,O)']. | 6863 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABD=32°, the center of circle O is O. Find ∠AOC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs withi... | consCDL:['Shape(BA,OAB)', 'Shape(AB,BD,DA)', 'Shape(AD,DC,CA)', 'Shape(AC,OCA)', 'Shape(CD,DO,OC)', 'Shape(CO,OD,DB,OBC)', 'Collinear(ADO)', 'Collinear(BDC)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(ABD),32)'], textCDL:['Equal(MeasureOfAngle(ABD),32)', 'IsCentreOfCircle(O,O)']. | 6881 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BAO=40°, ∠OHA=90°, O is the center of circle O. Find ∠ABC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all ... | consCDL:['Shape(AO,OH,HA)', 'Shape(AH,HC,OCA)', 'Shape(CH,HB,BC)', 'Shape(OBC,CB)', 'Shape(BH,HO,OA,OAB)', 'Collinear(OHC)', 'Collinear(AHB)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(BAO),40)', 'Equal(MeasureOfAngle(OHA),90)'], textCDL:['Equal(MeasureOfAngle(BAO),40)', 'Equal(MeasureOfAngle(OHA),90)', 'IsCe... | 6888 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAB=50°, O is the center of ⊙O, AB is the diameter of ⊙O, AB and AC are the legs of the isosceles triangle ABC. Find the measure of arc ODE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based... | consCDL:['Shape(OEA,AE)', 'Shape(EA,AD,ODE)', 'Shape(AO,OB,BD,DA)', 'Shape(ODE,DC,CE)', 'Shape(OBD,DB)', 'Collinear(BDC)', 'Collinear(AOB)', 'Collinear(AEC)', 'Cocircular(O,ABDE)'], imgCDL:['Equal(MeasureOfAngle(CAB),50)'], textCDL:['Equal(MeasureOfAngle(CAB),50)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)', '... | 6891 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ADC=25°, O is the center of circle O, the tangent to circle O is BA. Find the measure of ∠OBA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think... | consCDL:['Shape(OE,ED,ODC,CO)', 'Shape(OC,CE,EO)', 'Shape(EA,AD,DE)', 'Shape(EC,OCA,AE)', 'Shape(OAD,DA)', 'Shape(CB,BA,OCA)', 'Collinear(BCO)', 'Collinear(CED)', 'Collinear(OEA)', 'Cocircular(O,CAD)'], imgCDL:['Equal(MeasureOfAngle(ADC),25)'], textCDL:['Equal(MeasureOfAngle(ADC),25)', 'IsCentreOfCircle(O,O)', 'IsTange... | 6927 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABC=25°, O is the center of ⊙O. Find the measure of ∠AOC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all C... | consCDL:['Shape(OAB,BA)', 'Shape(OCA,AC)', 'Shape(AB,BD,DA)', 'Shape(AD,DC,CA)', 'Shape(DO,OC,CD)', 'Shape(OD,DB,OBC,CO)', 'Collinear(ADO)', 'Collinear(BDC)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(ABC),25)'], textCDL:['Equal(MeasureOfAngle(ABC),25)', 'IsCentreOfCircle(O,O)']. | 6933 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ACE=20°, O is the center of ⊙O, the diameter of circle O is AB. Find the measure of ∠BDE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></th... | consCDL:['Shape(OAC,CA)', 'Shape(OEA,AE)', 'Shape(ODE,ED)', 'Shape(OBD,DB)', 'Shape(AC,CF,FA)', 'Shape(AF,FG,GA)', 'Shape(AG,GE,EA)', 'Shape(FO,OB,BD,DG,GF)', 'Shape(GD,DE,EG)', 'Shape(OF,FC,OCB,BO)', 'Collinear(CFGE)', 'Collinear(AFOB)', 'Collinear(AGD)', 'Cocircular(O,ACBDE)'], imgCDL:['Equal(MeasureOfAngle(ACE),20)'... | 6940 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠COA=50°, O is the center of ⊙O, the tangent to ⊙O is AC. Find the measure of ∠ACD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> ta... | consCDL:['Shape(OC,OCD,DO)', 'Shape(OD,DC,CO)', 'Shape(ODC,CD)', 'Shape(DA,AC,ODC)', 'Collinear(ADO)', 'Cocircular(O,DC)'], imgCDL:['Equal(MeasureOfAngle(COA),50)'], textCDL:['Equal(MeasureOfAngle(COA),50)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(AC,O)']. | 6943 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AOB=120°, O is the center of ⊙O, the tangent to ⊙O is CA. Find the measure of ∠CAB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> t... | consCDL:['Shape(OAB,BO,OA)', 'Shape(AO,OB,BA)', 'Shape(AB,BD,ODA)', 'Shape(OBD,DB)', 'Shape(ODA,DC,CA)', 'Collinear(CDB)', 'Cocircular(O,BDA)'], imgCDL:[], textCDL:['Equal(MeasureOfAngle(AOB),120)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(CA,O)']. | 6991 |
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