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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.

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#### Solution

AB is the common chord in both the congruent circles.

∴ ∠APB = ∠AQB

In ΔBPQ,

∠APB = ∠AQB

∴ BQ = BP (Angles opposite to equal sides of a triangle)

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