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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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