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.

Let pointCandDbe the centres of the two congruent circles.LetABbe the common chord.∴arc AEB=arc AFBarcs of congruent chords of congruent circles∴∠APB=∠AQBangles subtended by congruent arcs (1)In△BPQ,∠APB=∠AQB...from (1)i.e.∠QPB=∠PQB∴BQ=BP...converse of isosceles triangle theorem