In the given figure, BC is a chord and CD is a tangent through the point C. If ∠AOC = 118°, then find the ∠ACD.

59°

Let us consider,

∠OCA = ∠OAC = a   [OA = OC = Radius]

In ∆AOC,

∠CAO + ∠ACO + ∠COA = 180°

= a + a + 118° = 180°

= 2a = 180° − 118° = 62°

= a = 31°

We know that,

So, ∠OCD = 90°

∠OCD = ∠ACO + ∠ACD

= ∠ACD + 31° = 90°

= ∠ACD = 90° − 31° = 59°