images images listlengths 1 1 | caption stringlengths 215 580 | cdl stringlengths 116 1.18k | proID stringlengths 1 4 | question stringlengths 8 110 | answer stringclasses 724
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<image>The Caption of this geometric diagram is:As shown in the diagram, ∠OBA=25°, O is the center of ⊙O. Find ∠ACB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(AO,OB,BA)', 'Shape(AC,CB,BO,OA)', 'Shape(OAC,CA)', 'Shape(OCB,BC)', 'Shape(OBA,AB)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(OBA),25)'], textCDL:['Equal(MeasureOfAngle(OBA),25)', 'IsCentreOfCircle(O,O)']. | 6914 | Find ∠ACB. | 65 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BCA=50°, O is the center of circle O, the diameter of circle O is AD. Find ∠DAB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(CA,AE,EC)', 'Shape(EA,AB,BE)', 'Shape(EB,BD,DO,OE)', 'Shape(OCA,AC)', 'Shape(OBD,DB)', 'Shape(OAB,BA)', 'Shape(ODC,CE,EO,OD)', 'Collinear(AEOD)', 'Collinear(BEC)', 'Cocircular(O,ABDC)'], imgCDL:['Equal(MeasureOfAngle(BCA),50)'], textCDL:['Equal(MeasureOfAngle(BCA),50)', 'IsCentreOfCircle(O,O)', 'IsDiame... | 6915 | Find ∠DAB. | 40 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAD=50°, the center of ⊙O is O, the diameter of ⊙O is AD. Find ∠ABC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(ED,DC,CE)', 'Shape(OE,EC,CA,AO)', 'Shape(BE,EO,OA,AB)', 'Shape(OCA,AC)', 'Shape(ODC,CD)', 'Shape(OAB,BA)', 'Shape(OBD,DE,EB)', 'Collinear(BEC)', 'Collinear(DEOA)', 'Cocircular(O,BDCA)'], imgCDL:['Equal(MeasureOfAngle(CAD),50)'], textCDL:['Equal(MeasureOfAngle(CAD),50)', 'IsCentreOfCircle(O,O)', 'IsDiame... | 6916 | Find ∠ABC. | 40 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BEO=90°, ∠CDB=70°, O is the center of circle O. Find ∠OAC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(DB,BO,OC,CD)', 'Shape(OB,BE,EO)', 'Shape(OE,EC,CO)', 'Shape(CE,EA,AC)', 'Shape(OAC,CA)', 'Shape(OCD,DC)', 'Shape(OBA,AE,EB)', 'Shape(ODB,BD)', 'Collinear(BEC)', 'Collinear(OEA)', 'Cocircular(O,DBAC)'], imgCDL:['Equal(MeasureOfAngle(BEO),90)', 'Equal(MeasureOfAngle(CDB),70)'], textCDL:['Equal(MeasureOfAn... | 6917 | Find ∠OAC. | 55 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABD=54°, the center of ⊙O is O, the diameter of ⊙O is AB. Find ∠DCB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(AE,ED,DA)', 'Shape(DE,EO,OB,BD)', 'Shape(BO,OE,EC,CB)', 'Shape(OAC,CE,EA)', 'Shape(ODA,AD)', 'Shape(OBD,DB)', 'Shape(OCB,BC)', 'Collinear(AEOB)', 'Collinear(DEC)', 'Cocircular(O,DACB)'], imgCDL:['Equal(MeasureOfAngle(ABD),54)'], textCDL:['Equal(MeasureOfAngle(ABD),54)', 'IsCentreOfCircle(O,O)', 'IsDiame... | 6918 | Find ∠DCB. | 36 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABO=40°, ∠COA=120°, ∠OAB=90°. Find ∠COB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(AB,BO,OA)', 'Shape(CO,OB)'], imgCDL:['Equal(MeasureOfAngle(ABO),40)', 'Equal(MeasureOfAngle(COA),120)', 'Equal(MeasureOfAngle(OAB),90)'], textCDL:['Equal(MeasureOfAngle(ABO),40)', 'Equal(MeasureOfAngle(COA),120)', 'Equal(MeasureOfAngle(OAB),90)']. | 6919 | Find ∠COB. | 70 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠OBC=35°, O is the center of ⊙O. 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. | consCDL:['Shape(AB,BO,OC,CA)', 'Shape(OB,BC,CO)', 'Shape(OCA,AC)', 'Shape(OAB,BA)', 'Shape(OBC,CB)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(OBC),35)'], textCDL:['Equal(MeasureOfAngle(OBC),35)', 'IsCentreOfCircle(O,O)']. | 6920 | Find the measure of ∠CAB. | 55 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, OA=2, ∠BCA=45°, the center of circle O is O. Find AB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(CA,AO,OB,BC)', 'Shape(OA,AB,BO)', 'Shape(OCA,AC)', 'Shape(OAB,BA)', 'Shape(OBC,CB)', 'Cocircular(O,CAB)'], imgCDL:['Equal(LengthOfLine(OA),2)', 'Equal(MeasureOfAngle(BCA),45)'], textCDL:['Equal(LengthOfLine(OA),2)', 'Equal(MeasureOfAngle(BCA),45)', 'IsCentreOfCircle(O,O)']. | 6922 | Find AB. | 2*sqrt(2) | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BOA=70°, the center of circle O is O. Find the measure of ∠BCA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OD,DC,OCA,AO)', 'Shape(OA,AD,DO)', 'Shape(DA,OAB,BD)', 'Shape(DB,BC,CD)', 'Shape(OBC,CB)', 'Collinear(ADC)', 'Collinear(ODB)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(BOA),70)'], textCDL:['Equal(MeasureOfAngle(BOA),70)', 'IsCentreOfCircle(O,O)']. | 6925 | Find the measure of ∠BCA. | 35 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, the center of ⊙O is O, AB is the diameter of ⊙O. Find the measure of ∠BCA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OB,BC,CA,AO)', 'Shape(OBC,CB)', 'Shape(OCA,AC)', 'Shape(OA,OAB,BO)', 'Collinear(AOB)', 'Cocircular(O,ABC)'], imgCDL:[], textCDL:['IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)']. | 6926 | Find the measure of ∠BCA. | 90 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CBE=56°, the center of ⊙O is O. Find the measure of ∠COA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(DA,AO,OC,CD)', 'Shape(ODA,AD)', 'Shape(OCD,DC)', 'Shape(OA,AB,BC,CO)', 'Shape(OAB,BA)', 'Shape(OBC,CB)', 'Collinear(ABE)', 'Cocircular(O,ABCD)'], imgCDL:['Equal(MeasureOfAngle(CBE),56)'], textCDL:['Equal(MeasureOfAngle(CBE),56)', 'IsCentreOfCircle(O,O)']. | 6928 | Find the measure of ∠COA. | 112 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAB=50°, O is the center of the inscribed circle of triangle ABC. Find the measure of ∠COB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(AB,BO,OA)', 'Shape(AO,OC,CA)', 'Shape(OB,BC,CO)'], imgCDL:['Equal(MeasureOfAngle(CAB),50)'], textCDL:['Equal(MeasureOfAngle(CAB),50)', 'IsIncenterOfTriangle(O,ABC)']. | 6929 | Find the measure of ∠COB. | 115 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BOC=56°, the center of ⊙O is O, C bisects segment AB. Find ∠ADB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OPA,AP)', 'Shape(OBP,PB)', 'Shape(PA,AO,OB,BP)', 'Shape(OA,AC,CO)', 'Shape(OC,CB,BO)', 'Shape(CA,AD,DB,BC)', 'Shape(OAD,DA)', 'Shape(ODB,BD)', 'Collinear(ACB)', 'Cocircular(O,ADBP)'], imgCDL:['Equal(MeasureOfAngle(BOC),56)'], textCDL:['Equal(MeasureOfAngle(BOC),56)', 'IsCentreOfCircle(O,O)', 'IsMidpoint... | 6931 | Find ∠ADB. | 124 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BCA=43°, O is the center of ⊙O. Find the measure of ∠BOA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OCA,AC)', 'Shape(CA,AO,OB,BC)', 'Shape(OBC,CB)', 'Shape(OA,OAB,BO)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(BCA),43)'], textCDL:['Equal(MeasureOfAngle(BCA),43)', 'IsCentreOfCircle(O,O)']. | 6934 | Find the measure of ∠BOA. | 86 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AOC=60°, the center of circle O is O, the diameter of circle O is BC. Find the measure of ∠OAB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OAB,BA)', 'Shape(BO,OA,AB)', 'Shape(OBC,CO,OB)', 'Shape(OC,OCA,AO)', 'Collinear(BOC)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(AOC),60)'], textCDL:['Equal(MeasureOfAngle(AOC),60)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(BC,O)']. | 6935 | Find the measure of ∠OAB. | 30 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, the center of circle O is O, AB is the diameter of circle O, D bisects arc OAB. Find ∠BCD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(AO,OE,EC,OCA)', 'Shape(OBC,CB)', 'Shape(CE,EB,BC)', 'Shape(OA,OAD,DO)', 'Shape(OD,DE,EO)', 'Shape(ED,ODB,BE)', 'Collinear(AOEB)', 'Collinear(DEC)', 'Cocircular(O,ADBC)'], imgCDL:[], textCDL:['IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)', 'IsMidpointOfArc(D,OAB)']. | 6936 | Find ∠BCD. | 45 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CDA=27°, the center of circle O is O, the tangent to ⊙O is BA. Find the measure of ∠ABC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OC,OCD,DO)', 'Shape(OD,DE,EO)', 'Shape(OE,EC,CO)', 'Shape(DA,AE,ED)', 'Shape(EA,OAC,CE)', 'Shape(ODA,AD)', 'Shape(OAC,AB,BC)', 'Collinear(DEC)', 'Collinear(OEA)', 'Collinear(OCB)', 'Cocircular(O,ACD)'], imgCDL:['Equal(MeasureOfAngle(CDA),27)'], textCDL:['Equal(MeasureOfAngle(CDA),27)', 'IsCentreOfCircle... | 6937 | Find the measure of ∠ABC. | 36 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAB=50°, O is the center of ⊙O, BE⊥OE. Find ∠CBD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OAB,BA)', 'Shape(OCA,AC)', 'Shape(AB,BE,EO,OA)', 'Shape(AO,OE,EC,CA)', 'Shape(BD,DE,EB)', 'Shape(ED,DC,CE)', 'Shape(OBD,DB)', 'Shape(ODC,CD)', 'Collinear(BEC)', 'Collinear(OED)', 'Cocircular(O,ABDC)'], imgCDL:['Equal(MeasureOfAngle(CAB),50)', 'PerpendicularBetweenLine(BE,OE)'], textCDL:['Equal(MeasureOf... | 6938 | Find ∠CBD. | 25 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ACB=70°, the center of circle O is O. Find ∠BAO. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OBA,AB)', 'Shape(OCB,BC)', 'Shape(BA,AD,DB)', 'Shape(BD,DC,CB)', 'Shape(DA,AO,OD)', 'Shape(OA,OAC,CD,DO)', 'Collinear(ADC)', 'Collinear(BDO)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(ACB),70)'], textCDL:['Equal(MeasureOfAngle(ACB),70)', 'IsCentreOfCircle(O,O)']. | 6939 | Find ∠BAO. | 20 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAB=35°, the center of ⊙O is O, the diameter of circle O is AB, CB is the tangent to circle O. Find ∠BCA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OAB,BO,OA)', 'Shape(ODA,AD)', 'Shape(AO,OB,OBD,DA)', 'Shape(OBD,BC,CD)', 'Collinear(ADC)', 'Collinear(AOB)', 'Cocircular(O,ABD)'], imgCDL:['Equal(MeasureOfAngle(CAB),35)'], textCDL:['Equal(MeasureOfAngle(CAB),35)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)', 'IsTangentOfCircle(CB,O)']. | 6941 | Find ∠BCA. | 55 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BPA=70°, O is the center of ⊙O, the tangent to circle O is PA, PB is the tangent to ⊙O. Find ∠OBA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(BO,OA,OAB)', 'Shape(OB,BA,AO)', 'Shape(OBA,AB)', 'Shape(BP,PA,OBA)', 'Cocircular(O,BA)'], imgCDL:['Equal(MeasureOfAngle(BPA),70)'], textCDL:['Equal(MeasureOfAngle(BPA),70)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(PA,O)', 'IsTangentOfCircle(PB,O)']. | 6944 | Find ∠OBA. | 35 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABC=50°, O is the center of circle O, the tangent to ⊙O is BA, AD is parallel to BO. Find ∠DCO. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OC,OCD,DE,EO)', 'Shape(OE,EC,CO)', 'Shape(DA,AE,ED)', 'Shape(EA,OAC,CE)', 'Shape(ODA,AD)', 'Shape(OAC,AB,BC)', 'Collinear(OCB)', 'Collinear(OEA)', 'Collinear(DEC)', 'Cocircular(O,ACD)'], imgCDL:['Equal(MeasureOfAngle(ABC),50)', 'ParallelBetweenLine(AD,BO)'], textCDL:['Equal(MeasureOfAngle(ABC),50)', 'Is... | 6945 | Find ∠DCO. | 20 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=3, BC=4, O is the center of circle O, the tangent to circle O is AG, the tangent to ⊙O is BH, FK is perpendicular to OK, quadrilateral ABCD is a rectangle. Find EF. Please provide the consCDL and imgCDL based on this given geometric diagram and... | consCDL:['Shape(AI,OEI,EA)', 'Shape(AG,OIG,IA)', 'Shape(GB,BH,OGH)', 'Shape(OG,OGH,HO)', 'Shape(OI,OIG,GO)', 'Shape(OEI,IO,OK,KE)', 'Shape(OFE,EK,KF)', 'Shape(FK,KO,OF)', 'Shape(OJF,FO,OJ)', 'Shape(OH,OHJ,JO)', 'Shape(OHJ,HC,CJ)', 'Shape(OJF,JC,CD,DF)', 'Collinear(AEKFD)', 'Collinear(AIOJC)', 'Collinear(AGB)', 'Colline... | 6946 | Find EF. | 6*sqrt(7)/7 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABC=25°, the center of ⊙O is O, AB is the tangent to ⊙O. Find ∠CDB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OBC,CB)', 'Shape(OCA,AC)', 'Shape(CA,AE,EC)', 'Shape(CE,EO,OC)', 'Shape(CO,OB,BC)', 'Shape(OAD,DE,EA)', 'Shape(OE,ED,DB,BO)', 'Shape(ODB,BD)', 'Collinear(CED)', 'Collinear(AEOB)', 'Cocircular(O,ADBC)'], imgCDL:['Equal(MeasureOfAngle(ABC),25)'], textCDL:['Equal(MeasureOfAngle(ABC),25)', 'IsCentreOfCircle... | 6947 | Find ∠CDB. | 65 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=sqrt(2), ∠CAB=30°, the radius of ⊙O is 1, 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. | consCDL:['Shape(OA,AD,DO)', 'Shape(OD,DC,OCA,AO)', 'Shape(AB,BD,DA)', 'Shape(DB,BC,CD)', 'Shape(OAB,BA)', 'Shape(OBC,CB)', 'Collinear(ADC)', 'Collinear(ODB)', 'Cocircular(O,ABC)'], imgCDL:['Equal(LengthOfLine(AB),sqrt(2))', 'Equal(MeasureOfAngle(CAB),30)'], textCDL:['Equal(LengthOfLine(AB),sqrt(2))', 'Equal(MeasureOfAn... | 6948 | Find ∠ABC. | 105 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CBA=70°, the center of circle O is O, AP is perpendicular to DP. Find the measure of ∠DEB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(ODE,ED)', 'Shape(OBD,DF,FB)', 'Shape(DE,EF,FD)', 'Shape(FP,PB,BF)', 'Shape(OEA,AP,PF,FE)', 'Shape(OAC,CP,PA)', 'Shape(PC,CB,BP)', 'Shape(OCB,BC)', 'Collinear(DFPC)', 'Collinear(APB)', 'Collinear(EFB)', 'Cocircular(O,ACBDE)'], imgCDL:['Equal(MeasureOfAngle(CBA),70)', 'PerpendicularBetweenLine(AP,DP)'], t... | 6949 | Find the measure of ∠DEB. | 20 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠COB=60°, O is the center of circle O, the diameter of ⊙O is AB. Find the measure of ∠OCA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OCA,AC)', 'Shape(AO,OC,CA)', 'Shape(OAB,BO,OA)', 'Shape(OBC,CO,OB)', 'Collinear(AOB)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(COB),60)'], textCDL:['Equal(MeasureOfAngle(COB),60)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)']. | 6951 | Find the measure of ∠OCA. | 30 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DCE=64°, the center of ⊙O is O. Find the measure of ∠DOB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(ODA,AD)', 'Shape(OAB,BA)', 'Shape(AB,BO,OD,DA)', 'Shape(OBC,CB)', 'Shape(OCD,DC)', 'Shape(OB,BC,CD,DO)', 'Collinear(BCE)', 'Cocircular(O,ABCD)'], imgCDL:['Equal(MeasureOfAngle(DCE),64)'], textCDL:['Equal(MeasureOfAngle(DCE),64)', 'IsCentreOfCircle(O,O)']. | 6953 | Find the measure of ∠DOB. | 128 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BAC=30°, O is the center of ⊙O, AO is perpendicular to CO. Find ∠AOB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OBA,AB)', 'Shape(OCB,BC)', 'Shape(AD,DB,BA)', 'Shape(BD,DC,CB)', 'Shape(AO,OD,DA)', 'Shape(DO,OC,CD)', 'Shape(OAC,CO,OA)', 'Collinear(ADC)', 'Collinear(ODB)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(BAC),30)', 'PerpendicularBetweenLine(AO,CO)'], textCDL:['Equal(MeasureOfAngle(BAC),30)', 'IsC... | 6954 | Find ∠AOB. | 30 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠APB=70°, the center of ⊙O is O, the tangent to ⊙O is PA, PB is the tangent to ⊙O. Find ∠ACB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(AP,PB,OCB,OAC)', 'Shape(OAC,CA)', 'Shape(OCB,BC)', 'Shape(AC,CB,BO,OA)', 'Shape(AO,OD,DA)', 'Shape(ODA,AD)', 'Shape(OB,BD,DO)', 'Shape(OBD,DB)', 'Cocircular(O,ACBD)'], imgCDL:['Equal(MeasureOfAngle(APB),70)'], textCDL:['Equal(MeasureOfAngle(APB),70)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(PA,O)', ... | 6956 | Find ∠ACB. | 125 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=CD, ∠BOA=42°, the center of ⊙O is O. Find ∠DEC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OF,FE,OEA,AO)', 'Shape(OAB,BA)', 'Shape(OA,AB,BO)', 'Shape(OB,OBC,CO)', 'Shape(OC,CF,FO)', 'Shape(FC,CD,DF)', 'Shape(EF,FD,DE)', 'Shape(ODE,ED)', 'Shape(OCD,DC)', 'Collinear(OFD)', 'Collinear(CFE)', 'Cocircular(O,ABCDE)'], imgCDL:['Equal(LengthOfLine(AB),LengthOfLine(CD))', 'Equal(MeasureOfAngle(BOA),42... | 6957 | Find ∠DEC. | 21 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, OA=3, △ABC is an equilateral △, the center of circle O is O, the diameter of circle O is AD. Find the length of arc OBD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OAB,BA)', 'Shape(OA,AB,BO)', 'Shape(AO,OE,EC,CA)', 'Shape(OCA,AC)', 'Shape(OB,BE,EO)', 'Shape(OBD,DB)', 'Shape(BD,DE,EB)', 'Shape(ODC,CE,ED)', 'Collinear(AOED)', 'Collinear(BEC)', 'Cocircular(O,ABDC)'], imgCDL:['Equal(LengthOfLine(OA),3)'], textCDL:['Equal(LengthOfLine(OA),3)', 'EquilateralTriangle(ABC)... | 6958 | Find the length of arc OBD. | pi | |
<image>The Caption of this geometric diagram is:As shown in the diagram, O is the center of ⊙O, ABCD is a square. Find ∠CPB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(ODA,AD)', 'Shape(DA,AO,OD)', 'Shape(OCD,DC)', 'Shape(DO,OC,CD)', 'Shape(OAP,PE,EA)', 'Shape(AE,EF,FO,OA)', 'Shape(OPB,BP)', 'Shape(PB,BE,EP)', 'Shape(OF,FC,CO)', 'Shape(EB,BF,FE)', 'Shape(FB,BC,CF)', 'Shape(OBC,CB)', 'Collinear(AOC)', 'Collinear(AEB)', 'Collinear(BFOD)', 'Collinear(PEFC)', 'Cocircular(O... | 6959 | Find ∠CPB. | 45 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAE=14°, the center of circle O is O, the diameter of circle O is AB, D bisects arc OCA. Find ∠BEC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(ODA,AD)', 'Shape(OCD,DC)', 'Shape(DA,AC,CD)', 'Shape(CA,AO,OB,BC)', 'Shape(OBC,CB)', 'Shape(OBC,BE,EC)', 'Shape(OA,OAB,BO)', 'Collinear(AOBE)', 'Collinear(DCE)', 'Cocircular(O,ABCD)'], imgCDL:['Equal(MeasureOfAngle(CAE),14)'], textCDL:['Equal(MeasureOfAngle(CAE),14)', 'IsCentreOfCircle(O,O)', 'IsDiamete... | 6960 | Find ∠BEC. | 24 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ACD=40°, the center of ⊙O is O, AB is the diameter of circle O. Find ∠DAB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(ODA,AD)', 'Shape(OCD,DC)', 'Shape(CD,DE,EC)', 'Shape(DA,AE,ED)', 'Shape(OBC,CE,EB)', 'Shape(EA,AO,OB,BE)', 'Shape(OA,OAB,BO)', 'Collinear(DEB)', 'Collinear(AEC)', 'Collinear(AOB)', 'Cocircular(O,ABCD)'], imgCDL:['Equal(MeasureOfAngle(ACD),40)'], textCDL:['Equal(MeasureOfAngle(ACD),40)', 'IsCentreOfCircl... | 6961 | Find ∠DAB. | 50 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BOA=60°, ∠OBC=55°, the center of ⊙O is O. Find the measure of ∠OAC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OCA,AO,OC)', 'Shape(OA,AD,DO)', 'Shape(OD,DC,CO)', 'Shape(DB,BC,CD)', 'Shape(OBC,CB)', 'Shape(OAB,BD,DA)', 'Collinear(ADC)', 'Collinear(ODB)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(BOA),60)', 'Equal(MeasureOfAngle(OBC),55)'], textCDL:['Equal(MeasureOfAngle(BOA),60)', 'Equal(MeasureOfAngle(... | 6962 | Find the measure of ∠OAC. | 25 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BOD=140°, the center of circle O is O, the diameter of ⊙O is AB. Find ∠DCA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OCA,AC)', 'Shape(CA,AE,EC)', 'Shape(CE,EO,OB,BC)', 'Shape(OBC,CB)', 'Shape(OAD,DE,EA)', 'Shape(OE,ED,DO)', 'Shape(OD,ODB,BO)', 'Collinear(AEOB)', 'Collinear(CED)', 'Cocircular(O,ADBC)'], imgCDL:['Equal(MeasureOfAngle(BOD),140)'], textCDL:['Equal(MeasureOfAngle(BOD),140)', 'IsCentreOfCircle(O,O)', 'IsDia... | 6963 | Find ∠DCA. | 20 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BCD=30°, O is the center of circle O, the diameter of circle O is AB. Find the measure of ∠DOA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OCA,AO,OE,EC)', 'Shape(OBC,CB)', 'Shape(BC,CE,EB)', 'Shape(OA,OAD,DO)', 'Shape(OD,DE,EO)', 'Shape(ED,ODB,BE)', 'Collinear(AOEB)', 'Collinear(CED)', 'Cocircular(O,ADBC)'], imgCDL:['Equal(MeasureOfAngle(BCD),30)'], textCDL:['Equal(MeasureOfAngle(BCD),30)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O... | 6964 | Find the measure of ∠DOA. | 120 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAB=40°, the center of ⊙O is O, the center of the circumscribed circle of triangle ABC is O. Find the measure of ∠COB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OAB,BA)', 'Shape(AB,BO,OC,CA)', 'Shape(OCA,AC)', 'Shape(OB,BC,CO)', 'Shape(OBC,CB)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(CAB),40)'], textCDL:['Equal(MeasureOfAngle(CAB),40)', 'IsCentreOfCircle(O,O)', 'IsCircumcenterOfTriangle(O,ABC)']. | 6967 | Find the measure of ∠COB. | 80 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABC=20°, O is the center of ⊙O, CD is the diameter of ⊙O. Find ∠DCA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OAD,DA)', 'Shape(ODB,BE,EO,OD)', 'Shape(AD,DO,OE,EA)', 'Shape(AE,EC,CA)', 'Shape(OCA,AC)', 'Shape(EB,BC,CE)', 'Shape(OBC,CB)', 'Collinear(DOEC)', 'Collinear(BEA)', 'Cocircular(O,ADBC)'], imgCDL:['Equal(MeasureOfAngle(ABC),20)'], textCDL:['Equal(MeasureOfAngle(ABC),20)', 'IsCentreOfCircle(O,O)', 'IsDiame... | 6969 | Find ∠DCA. | 70 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAB=50°, the center of circle O is O, E bisects segment BC. Find the measure of ∠CBD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OAB,BF,FA)', 'Shape(AF,FO,OE,EC,CA)', 'Shape(FB,BE,EO,OF)', 'Shape(OCA,AC)', 'Shape(OBD,DB)', 'Shape(EB,BD,DE)', 'Shape(ED,DC,CE)', 'Shape(ODC,CD)', 'Collinear(AFB)', 'Collinear(FOED)', 'Collinear(BEC)', 'Cocircular(O,ABDC)'], imgCDL:['Equal(MeasureOfAngle(CAB),50)'], textCDL:['Equal(MeasureOfAngle(CAB)... | 6971 | Find the measure of ∠CBD. | 25 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DCB=44°, O is the center of ⊙O, the diameter of circle O is AB. Find the measure of ∠ABD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(ODA,AD)', 'Shape(DA,AO,OE,ED)', 'Shape(OBD,DB)', 'Shape(DE,EB,BD)', 'Shape(OA,OAC,CE,EO)', 'Shape(EC,CB,BE)', 'Shape(OCB,BC)', 'Collinear(AOEB)', 'Collinear(DEC)', 'Cocircular(O,ACBD)'], imgCDL:['Equal(MeasureOfAngle(DCB),44)'], textCDL:['Equal(MeasureOfAngle(DCB),44)', 'IsCentreOfCircle(O,O)', 'IsDiame... | 6972 | Find the measure of ∠ABD. | 46 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAB=64°, the center of ⊙O is O. Find ∠BCO. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OCA,AC)', 'Shape(OAB,BA)', 'Shape(CA,AB,BO,OC)', 'Shape(CO,OB,BC)', 'Shape(OBC,CB)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(CAB),64)'], textCDL:['Equal(MeasureOfAngle(CAB),64)', 'IsCentreOfCircle(O,O)']. | 6975 | Find ∠BCO. | 26 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AD=AC, ∠BAD=30°, the center of ⊙O is O, AB is the diameter of circle O. Find the measure of ∠EOC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(ODB,BC,CD)', 'Shape(OAD,DA)', 'Shape(DC,CO,OA,AD)', 'Shape(OBE,EC,CB)', 'Shape(CE,EO,OC)', 'Shape(OE,EA,AO)', 'Shape(OEA,AE)', 'Collinear(BCOA)', 'Collinear(ECD)', 'Cocircular(O,BEAD)'], imgCDL:['Equal(LengthOfLine(AD),LengthOfLine(AC))', 'Equal(MeasureOfAngle(BAD),30)'], textCDL:['Equal(LengthOfLine(AD... | 6976 | Find the measure of ∠EOC. | 30 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠FOA=40°, O is the center of circle O, AB is the diameter of ⊙O. Find the measure of ∠BEF. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OEA,AC,CE)', 'Shape(OBE,EB)', 'Shape(EC,CO,OB,BE)', 'Shape(OAF,FC,CA)', 'Shape(CF,FO,OC)', 'Shape(OFB,BO,OF)', 'Collinear(ACOB)', 'Collinear(FCE)', 'Cocircular(O,AFBE)'], imgCDL:['Equal(MeasureOfAngle(FOA),40)'], textCDL:['Equal(MeasureOfAngle(FOA),40)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O... | 6979 | Find the measure of ∠BEF. | 70 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CBO=70°, O is the center of circle O, AB is the diameter of circle O, PA is the tangent to ⊙O, PO∥CB. Find the measure of ∠OPC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its capti... | consCDL:['Shape(AP,PD,OAD)', 'Shape(OAD,DO,OA)', 'Shape(DP,PC,ODC)', 'Shape(ODC,CO,OD)', 'Shape(OC,CB,BO)', 'Shape(OCB,BC)', 'Shape(OB,OBA,AO)', 'Collinear(AOB)', 'Collinear(PDO)', 'Cocircular(O,ADCB)'], imgCDL:['Equal(MeasureOfAngle(CBO),70)', 'ParallelBetweenLine(PO,CB)'], textCDL:['Equal(MeasureOfAngle(CBO),70)', 'I... | 6980 | Find the measure of ∠OPC. | 20 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=AC, ∠BCA=70°, the center of ⊙O is O, O is the center of the circumscribed circle of triangle ABC. Find the measure of ∠ABD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption... | consCDL:['Shape(OAB,BA)', 'Shape(AB,BO,OA)', 'Shape(AO,OD,DA)', 'Shape(OB,BE,EO)', 'Shape(DO,OC,CD)', 'Shape(OE,EC,CO)', 'Shape(OBC,CB)', 'Shape(OCA,AD,DC)', 'Collinear(ADC)', 'Collinear(BOD)', 'Collinear(AOE)', 'Collinear(BEC)', 'Cocircular(O,ABC)'], imgCDL:['Equal(LengthOfLine(AB),LengthOfLine(AC))', 'Equal(MeasureOf... | 6981 | Find the measure of ∠ABD. | 20 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CDA=20°, the center of circle O is O, AB is the diameter of circle O, the tangent to circle O is DC. Find the measure of ∠OAC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its captio... | consCDL:['Shape(OBA,AO,OB)', 'Shape(OA,AC,CO)', 'Shape(CA,OAC)', 'Shape(BO,OC,OCB)', 'Shape(OCB,CD,DB)', 'Collinear(AOBD)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(CDA),20)'], textCDL:['Equal(MeasureOfAngle(CDA),20)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)', 'IsTangentOfCircle(DC,O)']. | 6982 | Find the measure of ∠OAC. | 35 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠PAB=116°, O is the center of ⊙O, the diameter of ⊙O is BC, the tangent to ⊙O is PA. Find ∠CPA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OAB,BA)', 'Shape(AB,BO,OA)', 'Shape(AO,OC,OCA)', 'Shape(OCA,CP,PA)', 'Shape(CO,OB,OBC)', 'Collinear(BOCP)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(PAB),116)'], textCDL:['Equal(MeasureOfAngle(PAB),116)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(BC,O)', 'IsTangentOfCircle(PA,O)']. | 6983 | Find ∠CPA. | 38 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BAC=50°, O is the center of circle O, the tangent to ⊙O is AB, the tangent to ⊙O is AC. Find the measure of ∠CDB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(DC,OCD)', 'Shape(BD,ODB)', 'Shape(DB,BO,OC,CD)', 'Shape(CO,OB,OBC)', 'Shape(OBC,BA,AC)', 'Cocircular(O,DBC)'], imgCDL:['Equal(MeasureOfAngle(BAC),50)'], textCDL:['Equal(MeasureOfAngle(BAC),50)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(AB,O)', 'IsTangentOfCircle(AC,O)']. | 6984 | Find the measure of ∠CDB. | 65 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BCA=32°, O is the center of circle O, the diameter of ⊙O is BC. Find ∠ADC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OAB,BA)', 'Shape(AB,BE,EA)', 'Shape(AE,EO,OC,CA)', 'Shape(AC,OCA)', 'Shape(DE,EB,OBD)', 'Shape(ED,DC,CO,OE)', 'Shape(ODC,CD)', 'Collinear(BEOC)', 'Collinear(AED)', 'Cocircular(O,ABDC)'], imgCDL:['Equal(MeasureOfAngle(BCA),32)'], textCDL:['Equal(MeasureOfAngle(BCA),32)', 'IsCentreOfCircle(O,O)', 'IsDiame... | 6985 | Find ∠ADC. | 58 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠COA=60°, O is the center of circle O, AB is the diameter of circle O, D bisects ⌒OCB. Find ∠BAD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(AO,OB,OBA)', 'Shape(AE,EO,OA)', 'Shape(OE,ED,DO)', 'Shape(BO,OD,ODB)', 'Shape(CE,EA,OAC)', 'Shape(EC,OCD,DE)', 'Collinear(CEO)', 'Collinear(AED)', 'Collinear(AOB)', 'Cocircular(O,ACDB)'], imgCDL:['Equal(MeasureOfAngle(COA),60)'], textCDL:['Equal(MeasureOfAngle(COA),60)', 'IsCentreOfCircle(O,O)', 'IsDiam... | 6986 | Find ∠BAD. | 30 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BDA=60°, the center of circle O is O, the tangent to circle O is CA. Find the measure of ∠FCA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OAB,BA)', 'Shape(AB,BO,OA)', 'Shape(AO,OE,EA)', 'Shape(AE,EF,OFA)', 'Shape(OFA,FC,CA)', 'Shape(OBD,DB)', 'Shape(EO,OB,BD,DE)', 'Shape(FE,ED,ODF)', 'Collinear(BOEFC)', 'Collinear(AED)', 'Cocircular(O,ABDF)'], imgCDL:['Equal(MeasureOfAngle(BDA),60)'], textCDL:['Equal(MeasureOfAngle(BDA),60)', 'IsCentreOfC... | 6987 | Find the measure of ∠FCA. | 30 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DOB=140°, the center of circle O is O. 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. | consCDL:['Shape(BO,OD,ODB)', 'Shape(OB,BC,CD,DO)', 'Shape(OBC,CB)', 'Shape(OCD,DC)', 'Cocircular(O,BCD)'], imgCDL:['Equal(MeasureOfAngle(DOB),140)'], textCDL:['Equal(MeasureOfAngle(DOB),140)', 'IsCentreOfCircle(O,O)']. | 6988 | Find the measure of ∠BCD. | 110 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AO=4, OB=2, O is the center of circle O, the tangent to ⊙O is AC. Find AC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(ODC,DA,AC)', 'Shape(DO,OB,OBD)', 'Shape(CO,OD,ODC)', 'Shape(OC,CB,BO)', 'Shape(OCB,BC)', 'Collinear(ADOB)', 'Cocircular(O,DCB)'], imgCDL:['Equal(LengthOfLine(AO),4)', 'Equal(LengthOfLine(OB),2)'], textCDL:['Equal(LengthOfLine(AO),4)', 'Equal(LengthOfLine(OB),2)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCir... | 6989 | Find AC. | 2*sqrt(3) | |
<image>The Caption of this geometric diagram is:As shown in the diagram, O is the center of circle O, BA is the tangent to circle O, BC is the tangent to circle O, quadrilateral ABCD is a rhombus. Find the measure of ∠ABC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textC... | consCDL:['Shape(ODA,AD)', 'Shape(DA,AO,OC,CD)', 'Shape(CO,OA,OAC)', 'Shape(OCD,DC)', 'Shape(OAC,AB,BC)', 'Cocircular(O,ACD)'], imgCDL:[], textCDL:['IsCentreOfCircle(O,O)', 'IsTangentOfCircle(BA,O)', 'IsTangentOfCircle(BC,O)', 'Rhombus(ABCD)']. | 6992 | Find the measure of ∠ABC. | 60 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=AB, ∠BCD=26°, O is the center of circle O, the diameter of circle O is CD. Find the measure of ∠CBA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OAC,CA)', 'Shape(AC,CE,EA)', 'Shape(AE,EB,BA)', 'Shape(OBA,AB)', 'Shape(EC,CO,OD,DE)', 'Shape(BE,ED,ODB)', 'Shape(DO,OC,OCD)', 'Collinear(CEB)', 'Collinear(AED)', 'Collinear(COD)', 'Cocircular(O,ACDB)'], imgCDL:['Equal(LengthOfLine(AC),LengthOfLine(AB))', 'Equal(MeasureOfAngle(BCD),26)'], textCDL:['Equa... | 6994 | Find the measure of ∠CBA. | 32 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CDB=20°, the center of ⊙O is O, the diameter of ⊙O is AB. Find the measure of ∠EBC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OCA,AC)', 'Shape(CA,AO,OE,EC)', 'Shape(CE,EB,BC)', 'Shape(CB,OBC)', 'Shape(DE,EO,OA,OAD)', 'Shape(ED,DB,BE)', 'Shape(ODB,BD)', 'Collinear(AOEB)', 'Collinear(CED)', 'Cocircular(O,ADBC)'], imgCDL:['Equal(MeasureOfAngle(CDB),20)'], textCDL:['Equal(MeasureOfAngle(CDB),20)', 'IsCentreOfCircle(O,O)', 'IsDiame... | 6995 | Find the measure of ∠EBC. | 70 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠APB=40°, the center of circle O is O, PA is the tangent to ⊙O, PB is the tangent to circle O. Find the measure of ∠BCA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OAB,AP,PB)', 'Shape(OAB,BO,OA)', 'Shape(AO,OB,BC,CA)', 'Shape(OCA,AC)', 'Shape(OBC,CB)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(APB),40)'], textCDL:['Equal(MeasureOfAngle(APB),40)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(PA,O)', 'IsTangentOfCircle(PB,O)']. | 6996 | Find the measure of ∠BCA. | 70 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠EAO=25°, O is the center of circle O, AO⊥CO. 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. | consCDL:['Shape(OCA,AE,EC)', 'Shape(CE,ED,DC)', 'Shape(ODC,CD)', 'Shape(EA,AO,OE)', 'Shape(DE,EO,OB,OBD)', 'Shape(BO,OA,OAB)', 'Collinear(AOB)', 'Collinear(AED)', 'Collinear(CEO)', 'Cocircular(O,ABDC)'], imgCDL:['Equal(MeasureOfAngle(EAO),25)', 'PerpendicularBetweenLine(AO,CO)'], textCDL:['Equal(MeasureOfAngle(EAO),25)... | 6997 | Find the measure of ∠DCE. | 70 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠OBC=40°, O is the center of circle O, AB is the diameter of circle O. Find the measure of ∠EDB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(OCA,AC)', 'Shape(CA,AE,EC)', 'Shape(CE,EO,OB,BC)', 'Shape(OBC,CB)', 'Shape(DE,EA,OAD)', 'Shape(ED,DB,BO,OE)', 'Shape(ODB,BD)', 'Collinear(AEOB)', 'Collinear(CED)', 'Cocircular(O,ADBC)'], imgCDL:['Equal(MeasureOfAngle(OBC),40)'], textCDL:['Equal(MeasureOfAngle(OBC),40)', 'IsCentreOfCircle(O,O)', 'IsDiame... | 6998 | Find the measure of ∠EDB. | 50 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABD=15°, the center of circle O is O, the diameter of circle O is AB. 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. | consCDL:['Shape(OCD,DC)', 'Shape(CD,DE,EC)', 'Shape(AE,ED,ODA)', 'Shape(EA,AO,OB,BE)', 'Shape(CE,EB,BC)', 'Shape(OBC,CB)', 'Shape(BO,OA,OAB)', 'Collinear(DEB)', 'Collinear(AEC)', 'Collinear(AOB)', 'Cocircular(O,ABCD)'], imgCDL:['Equal(MeasureOfAngle(ABD),15)'], textCDL:['Equal(MeasureOfAngle(ABD),15)', 'IsCentreOfCircl... | 7000 | Find the measure of ∠BCD. | 105 |
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