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Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.

Q: 1    Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.

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Given: Circle C(P,r) and circle C(Q,r') intersect each other at A and B.

To prove : \anglePAQ = \anglePBQ 

Proof : In \triangleAPQ and \triangleBPQ,

                  PA = PB         (radii of same circle)

                 PQ = PQ        (Common)

                  QA = QB       (radii of same circle)

     So,           \triangleAPQ \cong \triangleBPQ       (By SSS)

                 \anglePAQ = \anglePBQ     (CPCT)

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