AB is a chord in the minor segment of a circle with centre O. C is a point on the minor arc (between A and B). The tangents to the circle at A and B meet at a point P. If ∠ACB = 108°, then ∠APB is equal to:
Show answer & explanation
Correct answer: A
Explanation
Given:
∠ACB = 108°
The tangents at A and B meet at P.
According to the formula:
Angle subtended at the circumference = Half the angle subtended at the center
Angle between the tangents = 180° − Central angle
∠ACB = 108°
Central angle (reflex) ∠AOB = 2 × 108° = 216°
Minor central angle = 360° − 216° = 144°
Now, the angle between the tangents:
∠APB = 180° − 144° = 36°