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Answer :
Given:
Two circles intersect at two points B and C. Through B two line segment ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively.
To prove: \(\angle{ACP}\) = \(\angle{QCD}\)
Proof:
In circle I,
\(\angle{ACP}\) = \(\angle{ABP}\) ...(i)
(Angles in the same segment)
In circle II,
\(\angle{QCD}\) = \(\angle{QBD}\) ...(ii)
(Angles in the same segment)
Also, \(\angle{ABP}\) = \(\angle{QBD}\)
(Vertically opposite angles)
From Equation (i) and (ii), we get,
\(\angle{ACP}\) = \(\angle{QCD}\)
Hence, proved.