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

Question

Philoid · Accepted Answer

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 = 60^o.

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

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

So OP = 2 AP