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. Prove that ∠ACP = ∠QCD.

⇒ChordsAPandDQare joined.⇒For chordAP,⇒∠PBA=∠ACP...Angles in the same segment — (i)⇒For chordDQ,⇒∠DBQ=∠QCD...Angles in same segment — (ii)⇒ABDandPBQare line segments intersecting atB.⇒∠PBA=∠DBQ...Vertically opposite angles — (iii)By the equations (i), (ii) and (iii),∠ACP=∠QCD