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Q 9. 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 $B P=B Q$.
Answers (1)
Given: 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.
To prove: BP = BQ
Proof:
AB is a common chord in both congruent circles.
$\therefore \angle A P B=\angle A Q B$
$\operatorname{In} \triangle B P Q$,
$\angle A P B=\angle A Q B$
$\therefore B Q=B P$ (Sides opposite to equal of the triangle are equal)
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