cles 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. Prove that ANGLE ACP= angle QCD. (SHORT ANSWER)⇒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=∠QCDGiven: Two circles intersect at two points B & C. Through B, two line segments ABD & PBQ are drawn which intersect the Circles at A, D, P & Q. To Prove: ∠ACP = ∠QCD Proof: In circle I, For chord AP, ∠PBA = ∠ACP (Angles in the same segment are equal) — (i) In circle II, 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 From the equations (i), (ii) and (iii), ∠ACP = ∠QCD HENCE THE ANSWER IS ∠ACP = ∠QCD:):)