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

56° 65° 59° 63°

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°