In the given figure, BC is a chord and CD is a tangent through the point C. If ∠AOC = 118°, then find the ∠ACD.
Answer & explanation
Correct answer: option 3
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°