Question

Two tangent segments PA and PB are drawn to a circle with centre O such that ∠APB = 120°. Prove that OP = 2 AP.

Answer 1

Let us first put the given data in the form of a diagram. We have,

Consider and . We have,

Here, PO is the common side.

PA = PB (Length of two tangents drawn from the same external point will be equal)

OA = OB(Radii of the same circle)

By SSS congruency, we have is congruent to .

Therefore,

It is given that,

That is,

(Since )

In ,

(Since radius will be perpendicular to the tangent at the point of contact)

We know that,

Thus we have proved.