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 the given figure). Prove that ∠ACP=∠QCD
Join chords AP and DQ.
For chord AP,
∠PBA=∠ACP (Angles in the same segment) ... (1)
For chord DQ,
∠DBQ=∠QCD (Angles in the same segment) ... (2)
ABD and PBQ are line segments intersecting at B.
∴∠PBA=∠DBQ (Vertically opposite angles) ... (3)
From equations (1), (2), and (3), we obtain