AB is a chord in a circle with center O. AB is produced to C such that BC is equal to the radius of the circle. C is joined to O and produced to meet the circle at D. If ∠ACD = 34°, then the measure of ∠AOD is ?

102°

OB = OC

⇒ ∠BOC = ∠BCO = 34°

We know, ∠OBA = ∠BOC + ∠BCO

= 34° + 34° = 68°

as OA = OB ⇒ ∠OAB = ∠OBA = 68°

In ΔOAB

∠AOB + 68° + 68° = 180°

∠AOB= 44°

Now, ∠AOD + 44° + 34° = 180°

∠AOB= 102°