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Question

Let M be a point of contact of two internally touching circles. Let line AMB be their common tangent.The chord CD of the bigger circle touches the smaller circle at point N and chord DM of the bigger circle touches the smaller circle at the points P and R respectively.
CMNDMN




Solution


Construction:- Join NR

CMA=CDM  (angles in the alternate segment)Let CMA=CDM=x............(1)NMA=NRM  (angles in the alternate segment)Let NMA=NRM=y  ...............(2)So, NMC=NMA-CMA=y-x .............(3)NMR=DNR  .......(4)         angles in alternate segmentsNRM is an exterior angle of NDRSo, NRM=NDR+DNR or,  y=CDM+DNR=x+DNRor, DNR=y-x ................5NMR=y-x              From (4) and (5)NMD =y-x........(6)CMN=DMN                  From 3 and 6           

Mathematics
Mathematics (Geometry)
Standard X

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