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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 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.

∴∠APB=∠AQB
In△BPQ,
∠APB=∠AQB
∴BQ=BP      (Sides opposite to equal of the triangle are equal)

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