Question

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 ∠ACD = 25°, then ∠AOD =?

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