Q9 of 35 Page 186

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.

AB is common chord in the given both triangles


So,


∠APB = ∠AQB


Now, in triangle BPQ


∠APB = ∠AQB


BQ = BP (Angles opposite to equal sides are equal)


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AC and BD are chords of a circle which bisect each other. Prove that:

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In any triangle ABC, if the angle bisector of ∠A and perpendicular bisector of BC intersect, prove that they intersect on the circum circle of the triangle ABC.