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# Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Fig. 10.40). Prove that ∠ACP = ∠ QCD.

Q : 9     Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Fig. $\small 10.40$). Prove that $\small \angle ACP=\angle QCD$.

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$\angle ABP=\angle QBD$................1(vertically opposite angles)

$\angle ACP=\angle ABP$..................2(Angles in the same segment are equal)

$\angle QBD=\angle QCD$.................3(angles in the same segment are equal)

From 1,2,3 ,we get

$\angle ACP=\angle QCD$

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