Question

WAITEMA
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 (see Fig. 10.40). Prove that
ZACP= Z QCD.
A​

Answer 1

Join chords AP 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