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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 : $\angle$PAQ = $\angle$PBQ

Proof : In $\triangle$APQ and $\triangle$BPQ,

PA = PB         (radii of same circle)

PQ = PQ        (Common)

QA = QB       (radii of same circle)

So,           $\triangle$APQ $\cong$ $\triangle$BPQ       (By SSS)

$\angle$PAQ = $\angle$PBQ     (CPCT)

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