The Total solution for NCERT class 6-12
Two circlesintersect at two points B and C. Through B, two line segments ABD and PBQ aredrawn to intersect the circles at A, D and P, Q respectively (see the givenfigure). Prove that ∠ACP = ∠QCD.
Join chordsAP and DQ.
For chord AP,
∠PBA = ∠ACP (Angles in the same segment) … (1)
For chord DQ,
∠DBQ = ∠QCD (Angles in the same segment) … (2)
ABD and PBQ are line segments intersecting at B.
∴ ∠PBA = ∠DBQ (Vertically opposite angles) … (3)
From equations (1), (2), and (3), we obtain
∠ACP = ∠QCD