CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
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



Open in App
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

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Intersection between Tangent and Secant
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon