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.