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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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Given : Two congruent circles which intersect at A and B. PAB is a line through A. 

To Prove : BP = BQ. 

Construction : Join AB. 

Proof : AB is a common chord of both the circles. 

But the circles are congruent — 

⇒arc ADB = arc AEB 

⇒ ∠APB = ∠AQB Angles subtended 

⇒ BP = BQ [Sides opposite to equal angles are equal] Proved.

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