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