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.

Question

Philoid · Accepted Answer

AB is common chord in the given both triangles

So,

∠APB = ∠AQB

Now, in triangle BPQ

∠APB = ∠AQB

BQ = BP (Angles opposite to equal sides are equal)