Hello, snigdha!

I used a (sort of) well-known theorem:

If a tangent and a secant are drawn to a circle from an external point,

the tangent is the mean proportional of the secant and the external segment of the secant.

is an isosceles triangle wherte

A circle through touches side at , and intersects side at .

If is the midpoint of , prove that: .Code:B ♥ o o o * * o o * * o o * * o * * o * * o o * ♥ P o* o * * * * o o * * o o * * o o * ♥ * * o ♥ o * * * * ♥ A D

We are given: .

is the midpoint of .[1]

From the theorem, we have: . .[2]

Substitute [1] into [2]: .

. . Therefore: .