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 ∠ACP = ∠QCD