Question

A
B В
16. In the given figure, AB is a chord of a
circle with centre 0 and AB is
produced to C such that BC = OB.
Also, CO is joined and produced to
meet the circle in D. If ZACD = yº and
ZAOD = xº, prove that x =
D
0
С
- 3y.​

Answer 1

In △OBC, OB = BC

⇒ ∠BOC = ∠BCO = y ...[angles opp. to equal sides are equal]

∠OBA is the exterior angle of △BOC

So, ∠ABO = 2y ...[ext. angle is equal to the sum of int. opp. angles]

Similarly, ∠AOD is the exterior angle of △AOC

∴ x = 2y + y = 3y