Question

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
angle ACP= angle QCD.​

Answer 1

Answer:

Prove that ∠ ACP =

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 = ∠QCD

0

votes

answered Dec 28, 2017 by navnit40 (-4,945 points)

∠ACP = ∠ABP ...i) [angles in the same segment]

∠QCD = ∠QBD ...ii) [angles in the same segment]

Also, ∠ABP = ∠QBD ...iii) [vertically opposite angles]

∴ From (i),(ii) and (iii), we have

∠ACP = ∠QCD