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 $B$.

$PAQ$ is a line segment

To prove: $BA=BQ$

Construction: Let us join $AB$

Proof:

$AB$ is a common chord of both the congruent circle.

A segment of both circles will be equal

$\angle P=\angle Q$

Now, in$∆BPQ,$

$\angle P=\angle Q$

$BP=BQ$ ——[sides opposite to equal angles are equal]

Hence the chord $BP=BQ$