Question

two tangent TP amd TQ are drawn to a circle with centre "O" from an external point T.prove that angle PTQ= 2ANGLE OPQ​

Answer 1

Answer:

Step-by-step explanation:

Draw a circle with centreO draw two tangents TP and TQ and locate that point as T where these tangents meet. Join TO,TP,TQ &PQ

  Proof-

       Let AnglePTQ= theta

       In triangleTPQ

         TP=TQ

       AngleTPQ=TQP AngleTPQ=AngleTQP= 1/2(180-theta)                        AngleOPT= 90degree

AngleOPQ= AngleOPT-OPT

         = 90-{90-1/2theta}

         = 90-90+1/2theta

         2AngleOPQ= anglePTQ

             Hence proved........