Two congruent circles intersect each other at point A and B.Through A any line segment PAQ is drawn so that P,Q lie on the two circles.Prove that BP = BQ. -Maths 9th

Two congruent circles intersect each other at point A and B.Through A any line segment PAQ is drawn so that P,Q lie on the two circles.Prove that BP = BQ. -Maths 9th
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Solution :- Let, O and O' be the centres of two congruent circles. As, AB is the common chord of these circles. ∴   ACB = ADB As congruent arcs subtent equal angles at the centre.    ∠AOB = ∠AO'B ⇒  1/2∠AOB = 1/2∠AO'B ⇒   ∠BPA = ∠BQA ⇒   BP = BQ (Sides opposite to equal angles)
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