**Given :** 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.

**To Prove : **∠ACP = ∠QCD.

**Proof : **∠ACP = ∠ABP ...(i) [Angles in the same segment]

∠QCD = ∠QBD ..(ii) [Angles in the same segment]

But, ∠ABP = ∠QBD ..(iii) [Vertically opposite angles]

By (i), (ii) and (ii) we get

∠ACP = ∠QCD **Proved**