Two circles touch internally at M. A straight line touches the inner circle at P and cuts the outer circle at Q and R. Prove that Angle QMP = Angle RMP..

Dear Student

Please find below the solution to the asked query

Construction:Draw a tangent to the circle at their point of contactSolution:Let SMQ = ythenSMQ = MRQ   Alternate segment theoremLet TPR = x then TPR = TMP= x     Alternate segment theorem.....(1)MPQ = x + y    Exterior angle of Δ RMPMPQ = MTP = x + y    Alternate segment theorem MTP = PMS = x+ y     Alternate segment theoremQMP = SMP -SMQ= x+ y y= x.......2From 1 and 2 we get TMP = QMP = xHence proved.....

Hope this information will clear your doubts about the topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.


  • 5
What are you looking for?