AB is a chord in the minor segment of a circle with center O. C is a point between A and B on the minor arc AB. The tangents to the circle at A and B meet at point D. If ∠ACB = 116°, then the measure of ∠ADB is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 52°
External ∠AOB = 2 × ∠ACB
⇒ External ∠AOB = 232°
Thus, ∠AOB = 360° - 232° = 128°
∠OAC = ∠OBC = 90°
In quadrilateral, ∠AOB + ∠OAC + ∠OBC + ∠APB = 360°
⇒ ∠APB = 360 - 90 - 90 - 128 = 360 - 308
⇒ ∠APB = 52°