Question

In fig common tangents PQ and RS to two circles intersect at A. Prove that PQ = RS.

Answer 1

Consider

Two circles namely (i) & (ii) as shown with common tangents as PQ and RS.

We know that

The tangents from external point to the circle are equal in length.

From A to circle (i) AP = AR … (i)

From A to circle (ii), AQ = AS …. (ii)

(i) + (ii) ⇒ AP + AQ = AR + RS

⇒ PQ = RS