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# 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.

Q: 9        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 $\small BP=BQ$.

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Given: 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.

To prove :  BP = BQ

Proof :

AB is a common chord in both congruent circles.

$\therefore \angle APB = \angle AQB$

In $\triangle BPQ,$

$\angle APB = \angle AQB$

$\therefore BQ = BP$      (Sides opposite to equal of the triangle are equal )

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