**Given : **Two congruent circles which intersect at A and B. PAB is a line through A.

**To Prove :** BP = BQ.

**Construction :** Join AB.

**Proof :** AB is a common chord of both the circles.

But the circles are congruent —

⇒arc ADB = arc AEB

⇒ ∠APB = ∠AQB Angles subtended

⇒ BP = BQ [Sides opposite to equal angles are equal] **Proved.**