Question

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.

Answer 1

Step-by-step explanation:

Chords AP and DQ are joined.

For chord AP,

∠PBA = ∠ACP (Angles in the same segment) --- (i)

For chord DQ,

∠DBQ = ∠QCD (Angles in same segment) --- (ii)

ABD and PBQ are line segments intersecting at B.

∠PBA = ∠DBQ (Vertically opposite angles) --- (iii)

By the equations (i), (ii) and (iii),

∠ACP = ∠QCD