images images listlengths 1 1 | problem stringlengths 310 675 | answer stringlengths 114 1.18k | proID stringlengths 1 4 |
|---|---|---|---|
<image>The Caption of this geometric diagram is:As shown in the diagram, CB=6, ∠CAB=60°, quadrilateral ABCD is a rhombus. 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 all CD... | consCDL:['Shape(DA,AE,ED)', 'Shape(EA,AB,BE)', 'Shape(DE,EC,CD)', 'Shape(CE,EB,BC)', 'Collinear(DEB)', 'Collinear(CEA)'], imgCDL:['Equal(LengthOfLine(CB),6)', 'Equal(MeasureOfAngle(CAB),60)'], textCDL:['Equal(LengthOfLine(CB),6)', 'Equal(MeasureOfAngle(CAB),60)', 'Rhombus(ABCD)']. | 143 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=x, AC=x, BC=5*sqrt(2), CA⊥BA. Find the value of x. 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 w... | consCDL:['Shape(AB,BC,CA)'], imgCDL:['Equal(LengthOfLine(AB),x)', 'Equal(LengthOfLine(AC),x)', 'Equal(LengthOfLine(BC),5*sqrt(2))', 'PerpendicularBetweenLine(CA,BA)'], textCDL:['Equal(LengthOfLine(AB),x)', 'Equal(LengthOfLine(AC),x)', 'Equal(LengthOfLine(BC),5*sqrt(2))', 'PerpendicularBetweenLine(CA,BA)']. | 144 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BA=5, ∠ABC=46°, B is the center of circle B. Find the area of the sector BCA. 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... | consCDL:['Shape(BCA,AB,BC)', 'Shape(BA,BAC,CB)', 'Cocircular(B,CA)'], imgCDL:['Equal(LengthOfLine(BA),5)', 'Equal(MeasureOfAngle(ABC),46)'], textCDL:['Equal(LengthOfLine(BA),5)', 'Equal(MeasureOfAngle(ABC),46)', 'IsCentreOfCircle(B,B)']. | 146 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, SR=5, TR=3, TS=4, RT is perpendicular to ST. Find the value of Sin(SRT). 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(TS,SR,RT)'], imgCDL:['Equal(LengthOfLine(SR),5)', 'Equal(LengthOfLine(TR),3)', 'Equal(LengthOfLine(TS),4)', 'PerpendicularBetweenLine(RT,ST)'], textCDL:['Equal(LengthOfLine(SR),5)', 'Equal(LengthOfLine(TR),3)', 'Equal(LengthOfLine(TS),4)', 'PerpendicularBetweenLine(RT,ST)']. | 148 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AF=1/2*y+20, CF=3*y, CG=20-3*x, FC=AF, HG=2*x-5, FG is parallel to AH. Find the value of x. 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(CF,FG,GC)', 'Shape(FA,AH,HG,GF)', 'Collinear(CFA)', 'Collinear(CGH)'], imgCDL:['Equal(LengthOfLine(AF),1/2*y+20)', 'Equal(LengthOfLine(CF),3*y)', 'Equal(LengthOfLine(CG),20-3*x)', 'Equal(LengthOfLine(FC),LengthOfLine(AF))', 'Equal(LengthOfLine(HG),2*x-5)', 'ParallelBetweenLine(FG,AH)'], textCDL:['Equal(... | 150 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BCA=5*x°, ∠DCB=3*x°. Find the value of x. 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(DC,CB)', 'Shape(BC,CA)', 'Collinear(DCA)'], imgCDL:['Equal(MeasureOfAngle(BCA),5*x)', 'Equal(MeasureOfAngle(DCB),3*x)'], textCDL:['Equal(MeasureOfAngle(BCA),5*x)', 'Equal(MeasureOfAngle(DCB),3*x)']. | 151 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ACF=140°, ∠IGE=9*x°, GD is parallel to CA. Find the value of x. 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(EG,GD)', 'Shape(DG,GC)', 'Shape(GC,CA)', 'Shape(AC,CF)', 'Shape(FC,CB)', 'Shape(BC,CG)', 'Shape(CG,GI)', 'Shape(IG,GE)', 'Collinear(IGD)', 'Collinear(BCA)', 'Collinear(EGCF)'], imgCDL:['Equal(MeasureOfAngle(ACF),140)', 'Equal(MeasureOfAngle(IGE),9*x)', 'ParallelBetweenLine(GD,CA)'], textCDL:['Equal(Meas... | 152 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DAF=4*x+5°, ∠FAB=9*x+20°, ∠FBC=4*y+4°, ∠FDA=y**2-1°, quadrilateral ABCD is a rectangle. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think... | consCDL:['Shape(AB,BF,FA)', 'Shape(FB,BC,CF)', 'Shape(FC,CD,DF)', 'Shape(AF,FD,DA)', 'Collinear(AFC)', 'Collinear(BFD)'], imgCDL:['Equal(MeasureOfAngle(DAF),4*x+5)', 'Equal(MeasureOfAngle(FAB),9*x+20)', 'Equal(MeasureOfAngle(FBC),4*y+4)', 'Equal(MeasureOfAngle(FDA),y**2-1)'], textCDL:['Equal(MeasureOfAngle(DAF),4*x+5)'... | 153 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AH=RH, HA=6-x, IJ=4/3*y+1, JE=2*y, RH=2*x+3, HJ is parallel to AE, RI∥HJ. Find the value of y. 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(RH,HJ,JI,IR)', 'Shape(HA,AE,EJ,JH)', 'Collinear(RHA)', 'Collinear(IJE)'], imgCDL:['Equal(LengthOfLine(AH),LengthOfLine(RH))', 'Equal(LengthOfLine(HA),6-x)', 'Equal(LengthOfLine(IJ),4/3*y+1)', 'Equal(LengthOfLine(JE),2*y)', 'Equal(LengthOfLine(RH),2*x+3)', 'ParallelBetweenLine(HJ,AE)', 'ParallelBetweenLi... | 154 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠WZY=4*x°, ∠XWZ=3*x°, ∠YXW=x°, ∠ZYX=2*x°. Find the measure of ∠ZYX. 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 prov... | consCDL:['Shape(XW,WZ,ZY,YX)'], imgCDL:['Equal(MeasureOfAngle(WZY),4*x)', 'Equal(MeasureOfAngle(XWZ),3*x)', 'Equal(MeasureOfAngle(YXW),x)', 'Equal(MeasureOfAngle(ZYX),2*x)'], textCDL:['Equal(MeasureOfAngle(WZY),4*x)', 'Equal(MeasureOfAngle(XWZ),3*x)', 'Equal(MeasureOfAngle(YXW),x)', 'Equal(MeasureOfAngle(ZYX),2*x)']. | 156 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BC=CE, CE=4*sqrt(2), the center of circle D is D, BE is the diameter of circle D, EC is perpendicular to BC. Find the circumference of the circle D. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCD... | consCDL:['Shape(DCB,BC)', 'Shape(DEC,CE)', 'Shape(CB,BD,DE,EC)', 'Shape(DB,DBE,ED)', 'Collinear(BDE)', 'Cocircular(D,CBE)'], imgCDL:['Equal(LengthOfLine(BC),LengthOfLine(CE))', 'Equal(LengthOfLine(CE),4*sqrt(2))', 'PerpendicularBetweenLine(EC,BC)'], textCDL:['Equal(LengthOfLine(BC),LengthOfLine(CE))', 'Equal(LengthOfLi... | 157 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠HPM=4*y°, ∠MPR=68°, ∠PRC=x°, ∠SCR=5*z+2°, MC∥PR, PM∥RC. Find the value of z. 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... | consCDL:['Shape(NC,CS)', 'Shape(SC,CR)', 'Shape(CR,RG)', 'Shape(GR,RJ)', 'Shape(JR,RP)', 'Shape(RP,PL)', 'Shape(LP,PH)', 'Shape(HP,PM)', 'Shape(PM,ME)', 'Shape(EM,MD)', 'Shape(DM,MC)', 'Shape(MC,CN)', 'Shape(CM,MP,PR,RC)', 'Collinear(NCRJ)', 'Collinear(DMPL)', 'Collinear(SCME)', 'Collinear(GRPH)'], imgCDL:['Equal(Measu... | 158 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DCG=3*x°, ∠GBA=x+24°, the center of circle O is O. Find ∠GBA. 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(OBA,AB)', 'Shape(GB,BA,AG)', 'Shape(OAD,DG,GA)', 'Shape(GD,DC,CG)', 'Shape(ODC,CD)', 'Shape(OCB,BG,GC)', 'Collinear(BGD)', 'Collinear(CGA)', 'Cocircular(O,BADC)'], imgCDL:['Equal(MeasureOfAngle(DCG),3*x)', 'Equal(MeasureOfAngle(GBA),x+24)'], textCDL:['Equal(MeasureOfAngle(DCG),3*x)', 'Equal(MeasureOfAng... | 159 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AE=6, DH=6, EF=6, AB⊥FB, DH is perpendicular to BH, EA is perpendicular to BA, FE⊥AE. Find the sum of Area(△DFB) and Area(FEAB). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its capti... | consCDL:['Shape(DF,FH,HD)', 'Shape(DH,HB,BD)', 'Shape(FE,EA,AB,BH,HF)', 'Collinear(FHB)'], imgCDL:['Equal(LengthOfLine(AE),6)', 'Equal(LengthOfLine(DH),6)', 'Equal(LengthOfLine(EF),6)', 'PerpendicularBetweenLine(AB,FB)', 'PerpendicularBetweenLine(DH,BH)', 'PerpendicularBetweenLine(EA,BA)', 'PerpendicularBetweenLine(FE,... | 161 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ANE=30°, ∠CEB=110°, ∠ECA=∠AFN, ∠ENJ=130°. Find the measure of ∠CAE. 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(CA,AE,EC)', 'Shape(EA,AN,NE)', 'Shape(AF,FN,NA)', 'Shape(CE,EB)', 'Shape(BE,EN)', 'Shape(EN,NJ)', 'Collinear(CAF)', 'Collinear(CEN)', 'Collinear(AEB)', 'Collinear(FNJ)'], imgCDL:['Equal(MeasureOfAngle(ANE),30)', 'Equal(MeasureOfAngle(CEB),110)', 'Equal(MeasureOfAngle(ECA),MeasureOfAngle(AFN))', 'Equal(M... | 162 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, KJ=11, KL=11, ML=5.5, ∠KJM=60°, KM⊥LM. Find the length of line JM. 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 provi... | consCDL:['Shape(KJ,JM,MK)', 'Shape(KM,ML,LK)', 'Collinear(JML)'], imgCDL:['Equal(LengthOfLine(KJ),11)', 'Equal(LengthOfLine(KL),11)', 'Equal(LengthOfLine(ML),5.5)', 'Equal(MeasureOfAngle(KJM),60)', 'PerpendicularBetweenLine(KM,LM)'], textCDL:['Equal(LengthOfLine(KJ),11)', 'Equal(LengthOfLine(KL),11)', 'Equal(LengthOfLi... | 163 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAD=42°, ∠CFG=77°, △CDE is an equilateral △, △CAB is an isosceles △, △CFG is an isosceles △. Find ∠GCF. 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(CA,AD,DC)', 'Shape(CD,DF,FC)', 'Shape(CF,FG,GC)', 'Shape(CG,GE,EC)', 'Shape(CE,EB,BC)', 'Collinear(ADFGEB)'], imgCDL:['Equal(MeasureOfAngle(CAD),42)', 'Equal(MeasureOfAngle(CFG),77)'], textCDL:['Equal(MeasureOfAngle(CAD),42)', 'Equal(MeasureOfAngle(CFG),77)', 'EquilateralTriangle(CDE)', 'IsoscelesTriang... | 164 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠LWX=53°, WL∥XE, XN∥ZK. Find the measure of ∠XZK. 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(GW,WL)', 'Shape(LW,WX)', 'Shape(WX,XE)', 'Shape(EX,XN)', 'Shape(NX,XZ)', 'Shape(XZ,ZK)', 'Shape(KZ,ZH)', 'Shape(HZ,ZY)', 'Shape(ZY,YM)', 'Shape(MY,YI)', 'Shape(IY,YW)', 'Shape(YW,WG)', 'Shape(WY,YZ,ZX,XW)', 'Collinear(GWXN)', 'Collinear(IYZK)', 'Collinear(LWYM)', 'Collinear(EXZH)'], imgCDL:['Equal(Measu... | 165 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=18, AD=24, BC=x, BD=9, ∠BAC=∠DAB. Find the value of x. 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 CD... | consCDL:['Shape(CB,BA,AC)', 'Shape(BD,DA,AB)', 'Collinear(CBD)'], imgCDL:['Equal(LengthOfLine(AC),18)', 'Equal(LengthOfLine(AD),24)', 'Equal(LengthOfLine(BC),x)', 'Equal(LengthOfLine(BD),9)', 'Equal(MeasureOfAngle(BAC),MeasureOfAngle(DAB))'], textCDL:['Equal(LengthOfLine(AC),18)', 'Equal(LengthOfLine(AD),24)', 'Equal(L... | 168 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠PSR=x+10°, ∠QPS=x°, ∠RQP=2*x-16°, ∠SRQ=2*x°. Find ∠SRQ. 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 CDL... | consCDL:['Shape(QP,PS,SR,RQ)'], imgCDL:['Equal(MeasureOfAngle(PSR),x+10)', 'Equal(MeasureOfAngle(QPS),x)', 'Equal(MeasureOfAngle(RQP),2*x-16)', 'Equal(MeasureOfAngle(SRQ),2*x)'], textCDL:['Equal(MeasureOfAngle(PSR),x+10)', 'Equal(MeasureOfAngle(QPS),x)', 'Equal(MeasureOfAngle(RQP),2*x-16)', 'Equal(MeasureOfAngle(SRQ),2... | 170 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AGC=60°, G is the center of ⊙G, DG is perpendicular to AG. Find ∠EGD. 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(GC,GCA,AG)', 'Shape(GA,GAD,DG)', 'Shape(GD,GDE,EG)', 'Shape(GE,GEB,BG)', 'Shape(GB,GBC,CG)', 'Collinear(AGB)', 'Collinear(CGE)', 'Cocircular(G,CADEB)'], imgCDL:['Equal(MeasureOfAngle(AGC),60)', 'PerpendicularBetweenLine(DG,AG)'], textCDL:['Equal(MeasureOfAngle(AGC),60)', 'IsCentreOfCircle(G,G)', 'Perpen... | 172 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠EAD=42°, the center of ⊙A is A. Find ⌒AEC. 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(AE,AEB,BA)', 'Shape(AB,ABC,CA)', 'Shape(AC,ACD,DA)', 'Shape(AD,ADE,EA)', 'Collinear(BAD)', 'Collinear(CAE)', 'Cocircular(A,BCDE)'], imgCDL:['Equal(MeasureOfAngle(EAD),42)'], textCDL:['Equal(MeasureOfAngle(EAD),42)', 'IsCentreOfCircle(A,A)']. | 174 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, CA=15, CB=x, ∠GBA=30°, C is the center of circle C, the tangent to ⊙C is BA. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <thi... | consCDL:['Shape(BA,CGA,GB)', 'Shape(AC,CG,CGA)', 'Shape(CA,CAG,GC)', 'Collinear(CGB)', 'Cocircular(C,AG)'], imgCDL:['Equal(LengthOfLine(CA),15)', 'Equal(LengthOfLine(CB),x)', 'Equal(MeasureOfAngle(GBA),30)'], textCDL:['Equal(LengthOfLine(CA),15)', 'Equal(LengthOfLine(CB),x)', 'Equal(MeasureOfAngle(GBA),30)', 'IsCentreO... | 175 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAD=42°, ∠CFG=77°, triangle CDE is an equilateral triangle, ∠CAB and ∠ABC are the base angles of the isosceles △ CAB, ∠CFG and ∠FGC are the base angles of the isosceles △ CFG. Find ∠FCD. Please provide the consCDL and imgCDL based on this given g... | consCDL:['Shape(CA,AD,DC)', 'Shape(CD,DF,FC)', 'Shape(CF,FG,GC)', 'Shape(CG,GE,EC)', 'Shape(CE,EB,BC)', 'Collinear(ADFGEB)'], imgCDL:['Equal(MeasureOfAngle(CAD),42)', 'Equal(MeasureOfAngle(CFG),77)'], textCDL:['Equal(MeasureOfAngle(CAD),42)', 'Equal(MeasureOfAngle(CFG),77)', 'EquilateralTriangle(CDE)', 'IsoscelesTriang... | 176 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, CB=18, CD=12, ∠BAD=115°, DA and CB are opposite sides of the parallelogram ADCB. Find ∠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></t... | consCDL:['Shape(AD,DC,CB,BA)'], imgCDL:['Equal(LengthOfLine(CB),18)', 'Equal(LengthOfLine(CD),12)', 'Equal(MeasureOfAngle(BAD),115)'], textCDL:['Equal(LengthOfLine(CB),18)', 'Equal(LengthOfLine(CD),12)', 'Equal(MeasureOfAngle(BAD),115)', 'Parallelogram(ADCB)']. | 178 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, QR=22, XY=15, XY is the midsegment of quadrilateral QTSR, QR and TS are the parallel sides of isosceles trapezoid QTSR. Find TS. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its capti... | consCDL:['Shape(QX,XY,YR,RQ)', 'Shape(XT,TS,SY,YX)', 'Collinear(QXT)', 'Collinear(RYS)'], imgCDL:['Equal(LengthOfLine(QR),22)', 'Equal(LengthOfLine(XY),15)'], textCDL:['Equal(LengthOfLine(QR),22)', 'Equal(LengthOfLine(XY),15)', 'IsMidsegmentOfQuadrilateral(XY,QTSR)', 'IsoscelesTrapezoid(QTSR)']. | 179 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠FHM=94°, HM is parallel to CA. Find the measure of ∠HCA. 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 CD... | consCDL:['Shape(FH,HM)', 'Shape(MH,HC)', 'Shape(HC,CA)', 'Shape(AC,CI)', 'Shape(IC,CE)', 'Shape(EC,CH)', 'Shape(CH,HD)', 'Shape(DH,HF)', 'Collinear(FHCI)', 'Collinear(MHD)', 'Collinear(ACE)'], imgCDL:['Equal(MeasureOfAngle(FHM),94)', 'ParallelBetweenLine(HM,CA)'], textCDL:['Equal(MeasureOfAngle(FHM),94)', 'ParallelBetw... | 180 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠YZW=60°, ∠ZWX=95°, V is the center of ⊙V. Find ∠XYZ. 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 w... | consCDL:['Shape(VZW,WZ)', 'Shape(VWX,XW)', 'Shape(VXY,YX)', 'Shape(VYZ,ZY)', 'Shape(ZW,WX,XY,YZ)', 'Cocircular(V,ZWXY)'], imgCDL:['Equal(MeasureOfAngle(YZW),60)', 'Equal(MeasureOfAngle(ZWX),95)'], textCDL:['Equal(MeasureOfAngle(YZW),60)', 'Equal(MeasureOfAngle(ZWX),95)', 'IsCentreOfCircle(V,V)']. | 181 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, CB∥DE. Prove that ∠TCB+∠EDG=180°. 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></CDL> ta... | consCDL:['Shape(TC,CB)', 'Shape(CD,DE,EB,BC)', 'Shape(ED,DG)', 'Collinear(TCDG)'], imgCDL:['ParallelBetweenLine(CB,DE)'], textCDL:['ParallelBetweenLine(CB,DE)']. | 184 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=27, BA=2*x+5, BA=BC, BC=3*x-4. Prove that ∠BCA and ∠CAB are the base angles of the isosceles △ BCA. 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(AB,BC,CA)'], imgCDL:['Equal(LengthOfLine(AC),27)', 'Equal(LengthOfLine(BA),2*x+5)', 'Equal(LengthOfLine(BA),LengthOfLine(BC))', 'Equal(LengthOfLine(BC),3*x-4)'], textCDL:['Equal(LengthOfLine(AC),27)', 'Equal(LengthOfLine(BA),2*x+5)', 'Equal(LengthOfLine(BA),LengthOfLine(BC))', 'Equal(LengthOfLine(BC),3*... | 187 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, the sum of the circumferences of circles A, B, and C is 42*pi, the radius of circle A is twice the radius of circle B, the radius of circle A is 4 times the radius of circle C, A is the center of ⊙A, the center of ⊙B is B, the center of ⊙C is C. F... | consCDL:['Shape(BD,BDE,EB)', 'Shape(BE,BED,DB)', 'Shape(CD)', 'Shape(C)', 'Shape(AE)', 'Shape(A)', 'Collinear(CDBEA)', 'Cocircular(C,D)', 'Cocircular(B,DE)', 'Cocircular(A,E)'], imgCDL:[], textCDL:['Equal(Add(PerimeterOfCircle(A),PerimeterOfCircle(B),PerimeterOfCircle(C)),42*pi)', 'Equal(RadiusOfCircle(A),Mul(RadiusOfC... | 188 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AE=12, AJ=15, ∠JBE=34°, ∠JCD=32°, J is the center of the inscribed circle of triangle CBA, AF is perpendicular to JF, CD is perpendicular to JD, JE⊥AE. Find ∠JAC. Please provide the consCDL and imgCDL based on this given geometric diagram and prov... | consCDL:['Shape(CD,DJ,JC)', 'Shape(DB,BJ,JD)', 'Shape(JB,BE,EJ)', 'Shape(JE,EA,AJ)', 'Shape(JA,AF,FJ)', 'Shape(JF,FC,CJ)', 'Collinear(CDB)', 'Collinear(BEA)', 'Collinear(AFC)'], imgCDL:['Equal(LengthOfLine(AE),12)', 'Equal(LengthOfLine(AJ),15)', 'Equal(MeasureOfAngle(JBE),34)', 'Equal(MeasureOfAngle(JCD),32)', 'Perpend... | 189 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠UVT=23°, D is the center of circle D. Find ⌒DTU. 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(DVT,TV)', 'Shape(VT,DTU,UV)', 'Shape(VU,DUV)', 'Cocircular(D,VTU)'], imgCDL:['Equal(MeasureOfAngle(UVT),23)'], textCDL:['Equal(MeasureOfAngle(UVT),23)', 'IsCentreOfCircle(D,D)']. | 190 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, VW=3*x-6, WX=x+4, YW=5, ZW=6, YX∥VZ. Find WX. 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 <C... | consCDL:['Shape(VZ,ZW,WV)', 'Shape(WX,XY,YW)', 'Collinear(ZWY)', 'Collinear(VWX)'], imgCDL:['Equal(LengthOfLine(VW),3*x-6)', 'Equal(LengthOfLine(WX),x+4)', 'Equal(LengthOfLine(YW),5)', 'Equal(LengthOfLine(ZW),6)', 'ParallelBetweenLine(YX,VZ)'], textCDL:['Equal(LengthOfLine(VW),3*x-6)', 'Equal(LengthOfLine(WX),x+4)', 'E... | 191 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=12, AC=y, AD=4, BC=x, CD=z, BA is perpendicular to CA, DC⊥BC. Find the value of x. 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(CB,BA,AC)', 'Shape(CA,AD,DC)', 'Collinear(BAD)'], imgCDL:['Equal(LengthOfLine(AB),12)', 'Equal(LengthOfLine(AC),y)', 'Equal(LengthOfLine(AD),4)', 'Equal(LengthOfLine(BC),x)', 'Equal(LengthOfLine(CD),z)', 'PerpendicularBetweenLine(BA,CA)', 'PerpendicularBetweenLine(DC,BC)'], textCDL:['Equal(LengthOfLine(... | 193 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=11, BC=x, ∠ABC=30°, ∠CAB=120°. Find the value of x. 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 ... | consCDL:['Shape(CA,AB,BC)'], imgCDL:['Equal(LengthOfLine(AC),11)', 'Equal(LengthOfLine(BC),x)', 'Equal(MeasureOfAngle(ABC),30)', 'Equal(MeasureOfAngle(CAB),120)'], textCDL:['Equal(LengthOfLine(AC),11)', 'Equal(LengthOfLine(BC),x)', 'Equal(MeasureOfAngle(ABC),30)', 'Equal(MeasureOfAngle(CAB),120)']. | 196 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠TWV=3*x-4°, ∠UTW=x°, ∠VUT=3*x-4°, ∠WVU=x°. Find ∠UTW. 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 ... | consCDL:['Shape(UT,TW,WV,VU)'], imgCDL:['Equal(MeasureOfAngle(TWV),3*x-4)', 'Equal(MeasureOfAngle(UTW),x)', 'Equal(MeasureOfAngle(VUT),3*x-4)', 'Equal(MeasureOfAngle(WVU),x)'], textCDL:['Equal(MeasureOfAngle(TWV),3*x-4)', 'Equal(MeasureOfAngle(UTW),x)', 'Equal(MeasureOfAngle(VUT),3*x-4)', 'Equal(MeasureOfAngle(WVU),x)'... | 197 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABD=x+14°, ∠ABF=3*x-8°, BD bisects ∠ABF. 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. You first think within <think></think> tags and then prov... | consCDL:['Shape(AB,BD)', 'Shape(DB,BF)', 'Shape(FB,BC)', 'Collinear(ABC)'], imgCDL:['Equal(MeasureOfAngle(ABD),x+14)', 'Equal(MeasureOfAngle(ABF),3*x-8)'], textCDL:['Equal(MeasureOfAngle(ABD),x+14)', 'Equal(MeasureOfAngle(ABF),3*x-8)', 'IsBisectorOfAngle(BD,ABF)']. | 198 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=3, AC=5, AE=y, BE=x, CD=7/2, DE=3, EB is parallel to DC. Find BE. 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(BA,AE,EB)', 'Shape(BE,ED,DC,CB)', 'Collinear(ABC)', 'Collinear(AED)'], imgCDL:['Equal(LengthOfLine(AB),3)', 'Equal(LengthOfLine(AC),5)', 'Equal(LengthOfLine(AE),y)', 'Equal(LengthOfLine(BE),x)', 'Equal(LengthOfLine(CD),7/2)', 'Equal(LengthOfLine(DE),3)', 'ParallelBetweenLine(EB,DC)'], textCDL:['Equal(Le... | 205 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, CE=ED, EC=6, EF=5, FE=EA, quadrilateral CFDA is a rhombus. Find Area(CFDA). 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 t... | consCDL:['Shape(CF,FE,EC)', 'Shape(EF,FD,DE)', 'Shape(ED,DA,AE)', 'Shape(CE,EA,AC)', 'Collinear(FEA)', 'Collinear(CED)'], imgCDL:['Equal(LengthOfLine(CE),LengthOfLine(ED))', 'Equal(LengthOfLine(EC),6)', 'Equal(LengthOfLine(EF),5)', 'Equal(LengthOfLine(FE),LengthOfLine(EA))'], textCDL:['Equal(LengthOfLine(CE),LengthOfLi... | 206 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=16, CD=23, ∠BDE=60°, DB and CA are opposite sides of the parallelogram BDCA, DE is perpendicular to BE. Find Area(BDCA). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. Y... | consCDL:['Shape(BD,DE,EB)', 'Shape(BE,EC,CA,AB)', 'Collinear(DEC)'], imgCDL:['Equal(LengthOfLine(AC),16)', 'Equal(LengthOfLine(CD),23)', 'Equal(MeasureOfAngle(BDE),60)', 'PerpendicularBetweenLine(DE,BE)'], textCDL:['Equal(LengthOfLine(AC),16)', 'Equal(LengthOfLine(CD),23)', 'Equal(MeasureOfAngle(BDE),60)', 'Parallelogr... | 207 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, LM=MN, ∠BNM=2*x-5°, the center of circle B is B, NL is the diameter of ⊙B. Find the value of x. 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(BML,LM)', 'Shape(BLN,NB,BL)', 'Shape(ML,LB,BN,NM)', 'Shape(BNM,MN)', 'Collinear(LBN)', 'Cocircular(B,LNM)'], imgCDL:['Equal(LengthOfLine(LM),LengthOfLine(MN))', 'Equal(MeasureOfAngle(BNM),2*x-5)'], textCDL:['Equal(LengthOfLine(LM),LengthOfLine(MN))', 'Equal(MeasureOfAngle(BNM),2*x-5)', 'IsCentreOfCircle... | 208 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BVC=52°, ∠VCB=6*x+14*y°, ∠ZXY=15*x-8*y°, ∠ZXY=∠BVC, CB⊥VB, XY⊥ZY. Find the value of y. 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(XY,YZ,ZX)', 'Shape(VC,CB,BV)'], imgCDL:['Equal(MeasureOfAngle(BVC),52)', 'Equal(MeasureOfAngle(VCB),6*x+14*y)', 'Equal(MeasureOfAngle(ZXY),15*x-8*y)', 'Equal(MeasureOfAngle(ZXY),MeasureOfAngle(BVC))', 'PerpendicularBetweenLine(CB,VB)', 'PerpendicularBetweenLine(XY,ZY)'], textCDL:['Equal(MeasureOfAngle(B... | 210 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=16, AC=5, BC=x, BC is perpendicular to AC. Find the value of x. 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 provi... | consCDL:['Shape(CA,AB,BC)'], imgCDL:['Equal(LengthOfLine(AB),16)', 'Equal(LengthOfLine(AC),5)', 'Equal(LengthOfLine(BC),x)', 'PerpendicularBetweenLine(BC,AC)'], textCDL:['Equal(LengthOfLine(AB),16)', 'Equal(LengthOfLine(AC),5)', 'Equal(LengthOfLine(BC),x)', 'PerpendicularBetweenLine(BC,AC)']. | 211 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BRS=103°, B is the center of circle B, TR is the tangent to ⊙B, the tangent to circle B is TS. Find ∠RTS. 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(BS,BSR,RB)', 'Shape(BR,BRS,SB)', 'Shape(BRS,RT,TS)', 'Cocircular(B,RS)'], imgCDL:['Equal(MeasureOfArc(BRS),103)'], textCDL:['Equal(MeasureOfArc(BRS),103)', 'IsCentreOfCircle(B,B)', 'IsTangentOfCircle(TR,B)', 'IsTangentOfCircle(TS,B)']. | 212 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABC=76°, ∠CAB= 1/2∠ABC. 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. You first think within <think></think> tags and then provide all CDLs with... | consCDL:['Shape(CA,AB,BC)'], imgCDL:['Equal(MeasureOfAngle(ABC),76)', 'Equal(MeasureOfAngle(CAB),Mul(MeasureOfAngle(ABC), 1/2))'], textCDL:['Equal(MeasureOfAngle(ABC),76)', 'Equal(MeasureOfAngle(CAB),Mul(MeasureOfAngle(ABC), 1/2))']. | 213 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, TV=TU, ∠VTU=74°. Find the measure of ∠TUV. 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(TU,UV,VT)'], imgCDL:['Equal(LengthOfLine(TV),LengthOfLine(TU))', 'Equal(MeasureOfAngle(VTU),74)'], textCDL:['Equal(LengthOfLine(TV),LengthOfLine(TU))', 'Equal(MeasureOfAngle(VTU),74)']. | 216 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=22, AC=14, BD=14, CD=22, E is the center of circle E, O is the center of circle O, AC is the diameter of circle O, BD is the diameter of circle E, OC⊥DC. Find the area of quadrilateral ACDB minus the sum of the areas of sectors OCA and EBD. Ple... | consCDL:['Shape(AO,OC,OCA)', 'Shape(OCA,CD,EBD,BA)', 'Shape(EBD,DE,EB)', 'Collinear(AOC)', 'Collinear(BED)', 'Cocircular(O,AC)', 'Cocircular(E,BD)'], imgCDL:['Equal(LengthOfLine(AB),22)', 'Equal(LengthOfLine(AC),14)', 'Equal(LengthOfLine(BD),14)', 'Equal(LengthOfLine(CD),22)', 'PerpendicularBetweenLine(OC,DC)'], textCD... | 217 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AM=MP, AP=sqrt(13), PD=3*sqrt(13), PN=ND, ∠MAB=∠NDC, the perimeter of △BPA is 12, CP is perpendicular to NP. Find Perimeter(△CPD). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its cap... | consCDL:['Shape(AB,BM,MA)', 'Shape(MB,BP,PM)', 'Shape(CP,PN,NC)', 'Shape(CN,ND,DC)', 'Collinear(AMPND)', 'Collinear(CPB)'], imgCDL:['Equal(LengthOfLine(AM),LengthOfLine(MP))', 'Equal(LengthOfLine(AP),sqrt(13))', 'Equal(LengthOfLine(PD),3*sqrt(13))', 'Equal(LengthOfLine(PN),LengthOfLine(ND))', 'Equal(MeasureOfAngle(MAB)... | 219 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AD=15, PF=6, the centroid of triangle ACE is P. Find AP. 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 CDL... | consCDL:['Shape(AB,BP,PA)', 'Shape(BC,CP,PB)', 'Shape(PC,CD,DP)', 'Shape(PD,DE,EP)', 'Shape(PE,EF,FP)', 'Shape(PF,FA,AP)', 'Collinear(ABC)', 'Collinear(CDE)', 'Collinear(EFA)', 'Collinear(BPE)', 'Collinear(CPF)', 'Collinear(APD)'], imgCDL:['Equal(LengthOfLine(AD),15)', 'Equal(LengthOfLine(PF),6)'], textCDL:['Equal(Leng... | 220 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠PSR=x+10°, ∠QPS=x°, ∠RQP=2*x-16°, ∠SRQ=2*x°. Find ∠PSR. 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 CDL... | consCDL:['Shape(QP,PS,SR,RQ)'], imgCDL:['Equal(MeasureOfAngle(PSR),x+10)', 'Equal(MeasureOfAngle(QPS),x)', 'Equal(MeasureOfAngle(RQP),2*x-16)', 'Equal(MeasureOfAngle(SRQ),2*x)'], textCDL:['Equal(MeasureOfAngle(PSR),x+10)', 'Equal(MeasureOfAngle(QPS),x)', 'Equal(MeasureOfAngle(RQP),2*x-16)', 'Equal(MeasureOfAngle(SRQ),2... | 221 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, XW=ZW, XY=ZY, ∠XWZ=70°, ∠ZYX=56°. Find the measure of ∠YXW. 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(XW,WZ,ZY,YX)'], imgCDL:['Equal(LengthOfLine(XW),LengthOfLine(ZW))', 'Equal(LengthOfLine(XY),LengthOfLine(ZY))', 'Equal(MeasureOfAngle(XWZ),70)', 'Equal(MeasureOfAngle(ZYX),56)'], textCDL:['Equal(LengthOfLine(XW),LengthOfLine(ZW))', 'Equal(LengthOfLine(XY),LengthOfLine(ZY))', 'Equal(MeasureOfAngle(XWZ),7... | 223 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, CN=8, N is the center of circle N. Find DN. 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(NDC,CN,ND)', 'Shape(NCF,FN,NC)', 'Shape(NF,FE,EN)', 'Shape(NED,DN,NE)', 'Shape(NFE,EN,NF)', 'Cocircular(N,DCFE)'], imgCDL:['Equal(LengthOfLine(CN),8)'], textCDL:['Equal(LengthOfLine(CN),8)', 'IsCentreOfCircle(N,N)']. | 225 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=20, AC=10, BC=x, ∠ABC=y°, BC is perpendicular to AC. Find the value of y. 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 ... | consCDL:['Shape(BC,CA,AB)'], imgCDL:['Equal(LengthOfLine(AB),20)', 'Equal(LengthOfLine(AC),10)', 'Equal(LengthOfLine(BC),x)', 'Equal(MeasureOfAngle(ABC),y)', 'PerpendicularBetweenLine(BC,AC)'], textCDL:['Equal(LengthOfLine(AB),20)', 'Equal(LengthOfLine(AC),10)', 'Equal(LengthOfLine(BC),x)', 'Equal(MeasureOfAngle(ABC),y... | 226 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=CB, DA=5*x-6, DC=3*x+4, BD⊥AD. 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 all CDLs within <CDL>... | consCDL:['Shape(AB,BD,DA)', 'Shape(BC,CD,DB)', 'Collinear(ADC)'], imgCDL:['Equal(LengthOfLine(AB),LengthOfLine(CB))', 'Equal(LengthOfLine(DA),5*x-6)', 'Equal(LengthOfLine(DC),3*x+4)', 'PerpendicularBetweenLine(BD,AD)'], textCDL:['Equal(LengthOfLine(AB),LengthOfLine(CB))', 'Equal(LengthOfLine(DA),5*x-6)', 'Equal(LengthO... | 228 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ACB=29°, ∠CBA=x°, ∠DAB=4*x°. Find the value of x. 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 with... | consCDL:['Shape(AC,CB,BA)', 'Shape(DA,AB)', 'Collinear(DAC)'], imgCDL:['Equal(MeasureOfAngle(ACB),29)', 'Equal(MeasureOfAngle(CBA),x)', 'Equal(MeasureOfAngle(DAB),4*x)'], textCDL:['Equal(MeasureOfAngle(ACB),29)', 'Equal(MeasureOfAngle(CBA),x)', 'Equal(MeasureOfAngle(DAB),4*x)']. | 229 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AHG=78°, A is the center of ⊙A, GB⊥HB, JH⊥GH. Find the measure of ∠HGB. 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(AGF,FB,BG)', 'Shape(AFJ,JA,AB,BF)', 'Shape(GB,BH,HG)', 'Shape(BA,AH,HB)', 'Shape(HA,AJ,JH)', 'Shape(AHG,GH)', 'Shape(AJH,HJ)', 'Collinear(FBH)', 'Collinear(GBAJ)', 'Cocircular(A,GFJH)'], imgCDL:['Equal(MeasureOfArc(AHG),78)', 'PerpendicularBetweenLine(GB,HB)', 'PerpendicularBetweenLine(JH,GH)'], textCDL... | 231 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AD=12, BD=4, AD is perpendicular to CD, DE⊥CE, EC is perpendicular to AC. 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></think> tag... | consCDL:['Shape(CA,AD,DC)', 'Shape(CD,DE,EC)', 'Shape(ED,DB,BE)', 'Collinear(ADB)', 'Collinear(CEB)'], imgCDL:['Equal(LengthOfLine(AD),12)', 'Equal(LengthOfLine(BD),4)', 'PerpendicularBetweenLine(AD,CD)', 'PerpendicularBetweenLine(DE,CE)', 'PerpendicularBetweenLine(EC,AC)'], textCDL:['Equal(LengthOfLine(AD),12)', 'Equa... | 232 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BEC=57°, DF∥HE, FE∥DH. Find ∠IFA. 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></CDL> t... | consCDL:['Shape(FD,DH,HE,EF)', 'Shape(BE,EC)', 'Shape(FE,EB)', 'Shape(AF,FE)', 'Shape(IF,FA)', 'Shape(DF,FI)', 'Shape(CE,EH)', 'Shape(GD,DF)', 'Shape(EH,HJ)', 'Shape(LD,DG)', 'Shape(HD,DL)', 'Shape(KH,HD)', 'Shape(JH,HK)', 'Collinear(AFDL)', 'Collinear(BEHK)', 'Collinear(IFEC)', 'Collinear(GDHJ)'], imgCDL:['Equal(Measu... | 234 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠NAP=120°, ∠PAQ=100°, the center of circle A is A. Find the measure of ∠QPN. 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 ... | consCDL:['Shape(APN,NP)', 'Shape(AP,PN,NA)', 'Shape(PA,AQ,QP)', 'Shape(AQP,PQ)', 'Shape(ANQ,QA,AN)', 'Cocircular(A,PNQ)'], imgCDL:['Equal(MeasureOfAngle(NAP),120)', 'Equal(MeasureOfAngle(PAQ),100)'], textCDL:['Equal(MeasureOfAngle(NAP),120)', 'Equal(MeasureOfAngle(PAQ),100)', 'IsCentreOfCircle(A,A)']. | 235 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠UTV=47°, RU is perpendicular to SU, TV⊥UV, VS is perpendicular to RS. Find ∠USR. 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(RU,US,SR)', 'Shape(SU,UV,VS)', 'Shape(VU,UT,TV)', 'Collinear(RUT)', 'Collinear(SVT)'], imgCDL:['Equal(MeasureOfAngle(UTV),47)', 'PerpendicularBetweenLine(RU,SU)', 'PerpendicularBetweenLine(TV,UV)', 'PerpendicularBetweenLine(VS,RS)'], textCDL:['Equal(MeasureOfAngle(UTV),47)', 'PerpendicularBetweenLine(RU... | 236 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, FB=9, FC=6, FD=6, FE=x, the center of ⊙A is A. Find the value of x. 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 prov... | consCDL:['Shape(AEC,CF,FE)', 'Shape(ADE,EF,FD)', 'Shape(ACB,BF,FC)', 'Shape(ABD,DF,FB)', 'Collinear(CFD)', 'Collinear(EFAB)', 'Cocircular(A,ECBD)'], imgCDL:['Equal(LengthOfLine(FB),9)', 'Equal(LengthOfLine(FC),6)', 'Equal(LengthOfLine(FD),6)', 'Equal(LengthOfLine(FE),x)'], textCDL:['Equal(LengthOfLine(FB),9)', 'Equal(L... | 237 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, TR=ST, ∠STR=50°. Find ∠TRS. 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></CDL> tags. | consCDL:['Shape(RS,ST,TR)'], imgCDL:['Equal(LengthOfLine(TR),LengthOfLine(ST))', 'Equal(MeasureOfAngle(STR),50)'], textCDL:['Equal(LengthOfLine(TR),LengthOfLine(ST))', 'Equal(MeasureOfAngle(STR),50)']. | 239 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=9*x-1, AF=2*x+7, ADCB is a rectangle. Find AF. 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(AD,DF,FA)', 'Shape(AF,FB,BA)', 'Shape(FD,DC,CF)', 'Shape(FC,CB,BF)', 'Collinear(AFC)', 'Collinear(DFB)'], imgCDL:['Equal(LengthOfLine(AC),9*x-1)', 'Equal(LengthOfLine(AF),2*x+7)'], textCDL:['Equal(LengthOfLine(AC),9*x-1)', 'Equal(LengthOfLine(AF),2*x+7)', 'Rectangle(ADCB)']. | 240 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, LR=10, PM=2KP, PR is parallel to KL, KN⊥MN, RM⊥PM. Find RM. 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(LR,RQ,QN,NL)', 'Shape(RM,MQ,QR)', 'Shape(QM,MP,PQ)', 'Shape(NQ,QP,PK,KN)', 'Collinear(LRM)', 'Collinear(MPK)', 'Collinear(LNK)', 'Collinear(RQP)', 'Collinear(NQM)'], imgCDL:['Equal(LengthOfLine(LR),10)', 'Equal(LengthOfLine(PM),Mul(LengthOfLine(KP),2))', 'ParallelBetweenLine(PR,KL)', 'PerpendicularBetwe... | 241 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, LR=3, RW=6, TR=8, TS is parallel to LW. Find WS. 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... | consCDL:['Shape(RW,WL,LR)', 'Shape(LW,WS,ST,TL)', 'Collinear(RLT)', 'Collinear(RWS)'], imgCDL:['Equal(LengthOfLine(LR),3)', 'Equal(LengthOfLine(RW),6)', 'Equal(LengthOfLine(TR),8)', 'ParallelBetweenLine(TS,LW)'], textCDL:['Equal(LengthOfLine(LR),3)', 'Equal(LengthOfLine(RW),6)', 'Equal(LengthOfLine(TR),8)', 'ParallelBe... | 242 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AVS=x°, ∠QVA=167°, ∠SVT=77°, ∠TVU=x°, ∠UVQ=26°, V is the center of ⊙V. Find the value of x. 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(VQU,UV,VQ)', 'Shape(VUT,TV,VU)', 'Shape(VTS,SV,VT)', 'Shape(VSA,AV,VS)', 'Shape(VAQ,QV,VA)', 'Cocircular(V,QUTSA)'], imgCDL:['Equal(MeasureOfAngle(AVS),x)', 'Equal(MeasureOfAngle(QVA),167)', 'Equal(MeasureOfAngle(SVT),77)', 'Equal(MeasureOfAngle(TVU),x)', 'Equal(MeasureOfAngle(UVQ),26)'], textCDL:['Equa... | 245 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BC=4, BF=x, ∠ABD=30°, ∠CBE=30°, ∠DBF=30°, ∠EBA=30°, BA⊥EA, BD⊥AD, BE is perpendicular to CE, BF is perpendicular to DF. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based ... | consCDL:['Shape(CB,BE,EC)', 'Shape(EB,BA,AE)', 'Shape(AB,BD,DA)', 'Shape(DB,BF,FD)'], imgCDL:['Equal(LengthOfLine(BC),4)', 'Equal(LengthOfLine(BF),x)', 'Equal(MeasureOfAngle(ABD),30)', 'Equal(MeasureOfAngle(CBE),30)', 'Equal(MeasureOfAngle(DBF),30)', 'Equal(MeasureOfAngle(EBA),30)', 'PerpendicularBetweenLine(BA,EA)', '... | 246 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=x, AC=6, BC=15, BC is perpendicular to AC. Find the value of x. 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 provi... | consCDL:['Shape(CA,AB,BC)'], imgCDL:['Equal(LengthOfLine(AB),x)', 'Equal(LengthOfLine(AC),6)', 'Equal(LengthOfLine(BC),15)', 'PerpendicularBetweenLine(BC,AC)'], textCDL:['Equal(LengthOfLine(AB),x)', 'Equal(LengthOfLine(AC),6)', 'Equal(LengthOfLine(BC),15)', 'PerpendicularBetweenLine(BC,AC)']. | 247 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BGC=40°, ∠DGF=53°, CB⊥GB, FG⊥CG, GF is perpendicular to DF. Find ∠FGB. 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(DG,GF,FD)', 'Shape(FG,GB,BA,AF)', 'Shape(BG,GC,CB)', 'Shape(AB,BC,CA)', 'Collinear(GBA)', 'Collinear(DFA)'], imgCDL:['Equal(MeasureOfAngle(BGC),40)', 'Equal(MeasureOfAngle(DGF),53)', 'PerpendicularBetweenLine(CB,GB)', 'PerpendicularBetweenLine(FG,CG)', 'PerpendicularBetweenLine(GF,DF)'], textCDL:['Equal... | 248 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, FQ=10, FW=x, WQ=4. Find the value of x. 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></C... | consCDL:['Shape(DF,FW,WB,BD)', 'Shape(ND,DB,BW,WQ,QC,CN)', 'Collinear(NDF)', 'Collinear(FWQ)'], imgCDL:['Equal(LengthOfLine(FQ),10)', 'Equal(LengthOfLine(FW),x)', 'Equal(LengthOfLine(WQ),4)'], textCDL:['Equal(LengthOfLine(FQ),10)', 'Equal(LengthOfLine(FW),x)', 'Equal(LengthOfLine(WQ),4)']. | 249 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=2, triangle DBC is an equilateral triangle, A is the center of circle A. Find the area of the ⊙A minus the area of triangle DBC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its ca... | consCDL:['Shape(ADB,BD)', 'Shape(DB,BA,AD)', 'Shape(AB,BC,CD,DA)', 'Shape(ACD,DC)', 'Shape(ABC,CB)', 'Cocircular(A,DBC)'], imgCDL:['Equal(LengthOfLine(AB),2)'], textCDL:['Equal(LengthOfLine(AB),2)', 'EquilateralTriangle(DBC)', 'IsCentreOfCircle(A,A)']. | 250 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, GF=5*x-9, GH=x+7, the center of circle J is J, GF is the tangent to ⊙J, the tangent to circle J is GH. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. Y... | consCDL:['Shape(JHF,HG,GF)', 'Shape(J)', 'Cocircular(J,FH)'], imgCDL:['Equal(LengthOfLine(GF),5*x-9)', 'Equal(LengthOfLine(GH),x+7)'], textCDL:['Equal(LengthOfLine(GF),5*x-9)', 'Equal(LengthOfLine(GH),x+7)', 'IsCentreOfCircle(J,J)', 'IsTangentOfCircle(GF,J)', 'IsTangentOfCircle(GH,J)']. | 253 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ZX=3*x+5, ZY=5*x-7, ∠ZWX=∠YWZ, WX is perpendicular to ZX, ZY is perpendicular to WY. Find XZ. 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(WX,XZ,ZW)', 'Shape(WZ,ZY,YW)'], imgCDL:['Equal(LengthOfLine(ZX),3*x+5)', 'Equal(LengthOfLine(ZY),5*x-7)', 'Equal(MeasureOfAngle(ZWX),MeasureOfAngle(YWZ))', 'PerpendicularBetweenLine(WX,ZX)', 'PerpendicularBetweenLine(ZY,WY)'], textCDL:['Equal(LengthOfLine(ZX),3*x+5)', 'Equal(LengthOfLine(ZY),5*x-7)', 'E... | 254 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, SR=5, TR=3, TS=4, RT⊥ST. Find the value of Cos(SRT). 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 wi... | consCDL:['Shape(TS,SR,RT)'], imgCDL:['Equal(LengthOfLine(SR),5)', 'Equal(LengthOfLine(TR),3)', 'Equal(LengthOfLine(TS),4)', 'PerpendicularBetweenLine(RT,ST)'], textCDL:['Equal(LengthOfLine(SR),5)', 'Equal(LengthOfLine(TR),3)', 'Equal(LengthOfLine(TS),4)', 'PerpendicularBetweenLine(RT,ST)']. | 255 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=x, AD=8, BD=y, ∠BCA=43°, CA⊥BA, DB is perpendicular to CB. Find the value of y. 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> tag... | consCDL:['Shape(DB,BA,AD)', 'Shape(AB,BC,CA)', 'Collinear(DAC)'], imgCDL:['Equal(LengthOfLine(AC),x)', 'Equal(LengthOfLine(AD),8)', 'Equal(LengthOfLine(BD),y)', 'Equal(MeasureOfAngle(BCA),43)', 'PerpendicularBetweenLine(CA,BA)', 'PerpendicularBetweenLine(DB,CB)'], textCDL:['Equal(LengthOfLine(AC),x)', 'Equal(LengthOfLi... | 256 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BDF=47°, ∠CIF=112°, ∠DFB=65°. Find the measure of ∠IAF. 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 CDL... | consCDL:['Shape(BD,DF,FB)', 'Shape(FI,IA,AF)', 'Shape(DB,BG)', 'Shape(BF,FA)', 'Shape(DF,FI)', 'Shape(CI,IF)', 'Collinear(GBFI)', 'Collinear(AFD)', 'Collinear(AIC)'], imgCDL:['Equal(MeasureOfAngle(BDF),47)', 'Equal(MeasureOfAngle(CIF),112)', 'Equal(MeasureOfAngle(DFB),65)'], textCDL:['Equal(MeasureOfAngle(BDF),47)', 'E... | 257 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=10, AE=25/4, BC=x+2, DE=x-1, △ABE is similar to △ACD.. Find BC. 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 provi... | consCDL:['Shape(AB,BE,EA)', 'Shape(BC,CD,DE,EB)', 'Collinear(ABC)', 'Collinear(AED)'], imgCDL:['Equal(LengthOfLine(AB),10)', 'Equal(LengthOfLine(AE),25/4)', 'Equal(LengthOfLine(BC),x+2)', 'Equal(LengthOfLine(DE),x-1)'], textCDL:['Equal(LengthOfLine(AB),10)', 'Equal(LengthOfLine(AE),25/4)', 'Equal(LengthOfLine(BC),x+2)'... | 259 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AD=5+x, BD=x, BF=5, CF=5+x, E is the center of circle E. Find the value of x. 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... | consCDL:['Shape(EDF,DB,BF)', 'Shape(EAD,DA)', 'Shape(EDF,FC,ECA,AD)', 'Shape(EFC,CF)', 'Collinear(BDA)', 'Collinear(BFC)', 'Cocircular(E,DFCA)'], imgCDL:['Equal(LengthOfLine(AD),5+x)', 'Equal(LengthOfLine(BD),x)', 'Equal(LengthOfLine(BF),5)', 'Equal(LengthOfLine(CF),5+x)'], textCDL:['Equal(LengthOfLine(AD),5+x)', 'Equa... | 260 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠FJH=82°, GFJH is a rhombus. Find ∠JHK. 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></C... | consCDL:['Shape(GF,FK,KG)', 'Shape(GK,KH,HG)', 'Shape(FJ,JK,KF)', 'Shape(KJ,JH,HK)', 'Collinear(FKH)', 'Collinear(GKJ)'], imgCDL:['Equal(MeasureOfAngle(FJH),82)'], textCDL:['Equal(MeasureOfAngle(FJH),82)', 'Rhombus(GFJH)']. | 262 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=13, AC=7, CB=10, FE=14, Triangle ACB is mirror similar to triangle DFE.. Find the perimeter of triangle DFE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first thi... | consCDL:['Shape(AC,CB,BA)', 'Shape(DF,FE,ED)'], imgCDL:['Equal(LengthOfLine(AB),13)', 'Equal(LengthOfLine(AC),7)', 'Equal(LengthOfLine(CB),10)', 'Equal(LengthOfLine(FE),14)'], textCDL:['Equal(LengthOfLine(AB),13)', 'Equal(LengthOfLine(AC),7)', 'Equal(LengthOfLine(CB),10)', 'Equal(LengthOfLine(FE),14)', 'MirrorSimilarBe... | 263 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CPD=3*x-15°, DP is perpendicular to AP, ADCB is a rhombus. Find the value of x. 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(AD,DP,PA)', 'Shape(AP,PB,BA)', 'Shape(PD,DC,CP)', 'Shape(PC,CB,BP)', 'Collinear(APC)', 'Collinear(DPB)'], imgCDL:['Equal(MeasureOfAngle(CPD),3*x-15)', 'PerpendicularBetweenLine(DP,AP)'], textCDL:['Equal(MeasureOfAngle(CPD),3*x-15)', 'PerpendicularBetweenLine(DP,AP)', 'Rhombus(ADCB)']. | 264 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠KFD=x°, ∠ECG=45°, ∠EDC=130°, E is the center of ⊙E. Find the value of x. 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(EDC,CD)', 'Shape(DC,CE,ED)', 'Shape(ECG,GE,EC)', 'Shape(EGK,KE,EG)', 'Shape(EKD,DE,EK)', 'Shape(EKD,KF,FD)', 'Collinear(GEKF)', 'Collinear(CDF)', 'Cocircular(E,CGKD)'], imgCDL:['Equal(MeasureOfAngle(KFD),x)', 'Equal(MeasureOfArc(ECG),45)', 'Equal(MeasureOfArc(EDC),130)'], textCDL:['Equal(MeasureOfAngle(... | 265 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AF=x+4, BD=x, BF=8, DC=2*x, the center of circle E is E. Find the value of x. 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... | consCDL:['Shape(EAF,FA)', 'Shape(ECA,AF,EFD,DC)', 'Shape(EDC,CD)', 'Shape(EFD,FB,BD)', 'Collinear(CDB)', 'Collinear(AFB)', 'Cocircular(E,AFDC)'], imgCDL:['Equal(LengthOfLine(AF),x+4)', 'Equal(LengthOfLine(BD),x)', 'Equal(LengthOfLine(BF),8)', 'Equal(LengthOfLine(DC),2*x)'], textCDL:['Equal(LengthOfLine(AF),x+4)', 'Equa... | 267 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BFD=165°, ∠CFB=x°, ∠DFC=145°, the center of ⊙F is F. Find the value of x. 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(FDB,BF,FD)', 'Shape(FBC,CF,FB)', 'Shape(FCD,DF,FC)', 'Cocircular(F,DBC)'], imgCDL:['Equal(MeasureOfAngle(BFD),165)', 'Equal(MeasureOfAngle(CFB),x)', 'Equal(MeasureOfAngle(DFC),145)'], textCDL:['Equal(MeasureOfAngle(BFD),165)', 'Equal(MeasureOfAngle(CFB),x)', 'Equal(MeasureOfAngle(DFC),145)', 'IsCentreOf... | 268 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, KL=AJ, ∠CKL=5*x°, ∠DJA=3*x+54°, Radius(⊙C) is equal to Radius(⊙D), the center of circle C is C, D is the center of ⊙D. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based o... | consCDL:['Shape(CKL,LK)', 'Shape(KL,LC,CK)', 'Shape(CLK,KC,CL)', 'Shape(DJA,AJ)', 'Shape(DJ,JA,AD)', 'Shape(DAJ,JD,DA)', 'Cocircular(C,KL)', 'Cocircular(D,JA)'], imgCDL:['Equal(LengthOfLine(KL),LengthOfLine(AJ))', 'Equal(MeasureOfArc(CKL),5*x)', 'Equal(MeasureOfArc(DJA),3*x+54)'], textCDL:['Equal(LengthOfLine(KL),Lengt... | 269 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=c, AC=b, CB=a, a=14, b=48, c=50, BC is perpendicular to AC. Find the value of Tan(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></th... | consCDL:['Shape(BC,CA,AB)'], imgCDL:['Equal(LengthOfLine(AB),c)', 'Equal(LengthOfLine(AC),b)', 'Equal(LengthOfLine(CB),a)', 'PerpendicularBetweenLine(BC,AC)'], textCDL:['Equal(LengthOfLine(AB),c)', 'Equal(LengthOfLine(AC),b)', 'Equal(LengthOfLine(CB),a)', 'Equal(a,14)', 'Equal(b,48)', 'Equal(c,50)', 'PerpendicularBetwe... | 270 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠FEC=a°, ∠GDA=b°, DH is perpendicular to EH. Find the value of a+b-90. 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(DH,HE,ED)', 'Shape(GD,DA)', 'Shape(FE,EC)', 'Collinear(ADH)', 'Collinear(HEF)', 'Collinear(GDEC)'], imgCDL:['Equal(MeasureOfAngle(FEC),a)', 'Equal(MeasureOfAngle(GDA),b)', 'PerpendicularBetweenLine(DH,EH)'], textCDL:['Equal(MeasureOfAngle(FEC),a)', 'Equal(MeasureOfAngle(GDA),b)', 'PerpendicularBetweenLi... | 271 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABG=47°, ∠ACG=136°, ∠BED=63°, ∠DFB=∠BDF, ∠EBA=69°. 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. You first think within <think></think> tags and... | consCDL:['Shape(ED,DB,BE)', 'Shape(BD,DF,FB)', 'Shape(AB,BC,CA)', 'Shape(EB,BA)', 'Shape(AC,CG)', 'Collinear(DBCG)', 'Collinear(EBF)'], imgCDL:['Equal(MeasureOfAngle(ABG),47)', 'Equal(MeasureOfAngle(ACG),136)', 'Equal(MeasureOfAngle(BED),63)', 'Equal(MeasureOfAngle(DFB),MeasureOfAngle(BDF))', 'Equal(MeasureOfAngle(EBA)... | 273 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ADC=60°, D is the center of circle D. 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. You first think within <think></think> tags and then provide... | consCDL:['Shape(DAB,BA)', 'Shape(DBC,CB)', 'Shape(DCA,AD,DC)', 'Shape(DA,AB,BC,CD)', 'Cocircular(D,ABC)'], imgCDL:['Equal(MeasureOfAngle(ADC),60)'], textCDL:['Equal(MeasureOfAngle(ADC),60)', 'IsCentreOfCircle(D,D)']. | 274 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, DC=6-x, DG=2, JL=4, JM=x, DG is the altitude of △ DEC, JM is the altitude of triangle JKL, DG is perpendicular to CG, JM is perpendicular to LM, triangle KLJ is similar to triangle ECD.. Find DC. Please provide the consCDL and imgCDL based on this... | consCDL:['Shape(JK,KM,MJ)', 'Shape(JM,ML,LJ)', 'Shape(DE,EG,GD)', 'Shape(DG,GC,CD)', 'Collinear(KML)', 'Collinear(EGC)'], imgCDL:['Equal(LengthOfLine(DC),6-x)', 'Equal(LengthOfLine(DG),2)', 'Equal(LengthOfLine(JL),4)', 'Equal(LengthOfLine(JM),x)', 'PerpendicularBetweenLine(DG,CG)', 'PerpendicularBetweenLine(JM,LM)'], t... | 275 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BA=3, BD=x-1, CE=x+2, EF=8, ∠GAB=∠EFG, AB is perpendicular to CB, DE is perpendicular to FE. Find EC. 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(AB,BC,CG,GA)', 'Shape(GC,CD,DG)', 'Shape(GD,DE,EF,FG)', 'Collinear(BCDE)', 'Collinear(AGD)', 'Collinear(CGF)'], imgCDL:['Equal(LengthOfLine(BA),3)', 'Equal(LengthOfLine(BD),x-1)', 'Equal(LengthOfLine(CE),x+2)', 'Equal(LengthOfLine(EF),8)', 'Equal(MeasureOfAngle(GAB),MeasureOfAngle(EFG))', 'Perpendicular... | 276 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=5, BC=3, AC⊥BC. 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 within <think></think> tags and then provide all CDLs within <CDL></CDL> tags. | consCDL:['Shape(AC,CB,BA)'], imgCDL:['Equal(LengthOfLine(AC),5)', 'Equal(LengthOfLine(BC),3)', 'PerpendicularBetweenLine(AC,BC)'], textCDL:['Equal(LengthOfLine(AC),5)', 'Equal(LengthOfLine(BC),3)', 'PerpendicularBetweenLine(AC,BC)']. | 277 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, the area of triangle CEA is 52, CD=b+5, EA=b, ED is perpendicular to CD. Find the value of b. 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(CE,ED,DC)', 'Shape(CD,DA,AC)', 'Collinear(EDA)'], imgCDL:['Equal(LengthOfLine(CD),b+5)', 'Equal(LengthOfLine(EA),b)', 'PerpendicularBetweenLine(ED,CD)'], textCDL:['Equal(AreaOfTriangle(CEA),52)', 'Equal(LengthOfLine(CD),b+5)', 'Equal(LengthOfLine(EA),b)', 'PerpendicularBetweenLine(ED,CD)']. | 278 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, EI=18, FH=37, GB=9, GB⊥HB, IE⊥FE. Find the sum of the area of triangle IHF and Area(△FHG). 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(GF,FE,EB,BG)', 'Shape(FI,IE,EF)', 'Shape(EI,IH,HB,BE)', 'Shape(GB,BH,HG)', 'Collinear(FEBH)'], imgCDL:['Equal(LengthOfLine(EI),18)', 'Equal(LengthOfLine(FH),37)', 'Equal(LengthOfLine(GB),9)', 'PerpendicularBetweenLine(GB,HB)', 'PerpendicularBetweenLine(IE,FE)'], textCDL:['Equal(LengthOfLine(EI),18)', 'E... | 279 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=9, AY=18, PO=x, QP=y, RO=14, YB=21, RQPO is similar to BCAY. Find the value of y. 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(RQ,QP,PO,OR)', 'Shape(AY,YB,BC,CA)'], imgCDL:['Equal(LengthOfLine(AC),9)', 'Equal(LengthOfLine(AY),18)', 'Equal(LengthOfLine(PO),x)', 'Equal(LengthOfLine(QP),y)', 'Equal(LengthOfLine(RO),14)', 'Equal(LengthOfLine(YB),21)'], textCDL:['Equal(LengthOfLine(AC),9)', 'Equal(LengthOfLine(AY),18)', 'Equal(Lengt... | 280 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=8, AD=4, CB=10, AC⊥BC, DA is perpendicular to CA. Find the area of quadrilateral ACBD. 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(BD,DA,AC,CB)'], imgCDL:['Equal(LengthOfLine(AC),8)', 'Equal(LengthOfLine(AD),4)', 'Equal(LengthOfLine(CB),10)', 'PerpendicularBetweenLine(AC,BC)', 'PerpendicularBetweenLine(DA,CA)'], textCDL:['Equal(LengthOfLine(AC),8)', 'Equal(LengthOfLine(AD),4)', 'Equal(LengthOfLine(CB),10)', 'PerpendicularBetweenLin... | 286 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BA=15, CB=12, CA=x, the center of ⊙A is A, the tangent to ⊙A is BC. Find the value of x. 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(ACF,FA,AC)', 'Shape(AFC,CA,AF)', 'Shape(ACF,CB,BF)', 'Collinear(BFA)', 'Cocircular(A,CF)'], imgCDL:['Equal(LengthOfLine(BA),15)', 'Equal(LengthOfLine(CB),12)', 'Equal(LengthOfLine(CA),x)'], textCDL:['Equal(LengthOfLine(BA),15)', 'Equal(LengthOfLine(CB),12)', 'Equal(LengthOfLine(CA),x)', 'IsCentreOfCircl... | 288 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BGC=100°, ∠DCF=75°. Find ∠GAC. 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></CDL> tags... | consCDL:['Shape(GA,AC,CG)', 'Shape(BG,GC)', 'Shape(DC,CF)', 'Collinear(EGCF)', 'Collinear(AGB)', 'Collinear(ACD)'], imgCDL:['Equal(MeasureOfAngle(BGC),100)', 'Equal(MeasureOfAngle(DCF),75)'], textCDL:['Equal(MeasureOfAngle(BGC),100)', 'Equal(MeasureOfAngle(DCF),75)']. | 289 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=BY, AB=x, AY=8, ∠YAB=y°, AB⊥YB. Find the value of x. 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... | consCDL:['Shape(AB,BY,YA)'], imgCDL:['Equal(LengthOfLine(AB),LengthOfLine(BY))', 'Equal(LengthOfLine(AB),x)', 'Equal(LengthOfLine(AY),8)', 'Equal(MeasureOfAngle(YAB),y)', 'PerpendicularBetweenLine(AB,YB)'], textCDL:['Equal(LengthOfLine(AB),LengthOfLine(BY))', 'Equal(LengthOfLine(AB),x)', 'Equal(LengthOfLine(AY),8)', 'E... | 292 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.