Q13 of 93 Page 10

Two tangent segments PA and PB are drawn to a circle with centre O such that . Prove that OP = 2 AP.

PA = PB (Tangents from external point)


OA = OB (Radii of same circle )


OP = OP (common)


Triangle OAP is similar to triangle OBP ( By SSS criterion)


Angle OPA = angle OPB = 60o.


In Triangle OAP , the angle OAP = 90o(By Theorem)


sin 60o= AP / OP , i.e 1/2 = AP / OP


So OP = 2 AP


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