Question

A
B
25°
C
D
o
11. In the given figure, AB is a chord of a circle with
centre O and AB is produced to C such that
BC =OB. Also, CO is joined and produced to
meet the circle in D. If ZACD = 25°, then
ZAOD = ?
(a) 50°
(b) 75°
(c) 90°
(d) 100°​

Answer 1

Step-by-step explanation:

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