Question

PROVE THIS......
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Answer 1

Given: 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),

Thus, ∠ACP = ∠QCD

Hence Proved.