Q36 of 62 Page 10

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.

Given: Two congruent circles intersect each other at points A and B. A line through A meets the circles in P and Q.
 
Proof:  AB is the common chord of the two congruent circles
∴ ∠ APB = ∠ AQB       | Since angles subtended by equal chords are equal
∴ BP = BQ.                | Sides opposite to equal angles are equal

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