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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.

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 \small BP=BQ.

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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 APB = \angle AQB

In \triangle BPQ,

   \angle APB = \angle AQB

    \therefore BQ = BP      (Sides opposite to equal of the triangle are equal )

 

 

 

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