Question

Two congruent circles intersect each other at points A and B. Through A any line segment PAQ is drawn so that P, Q lie on the two circles. Prove that BP = BQ

Answer 1

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.