In a circle with centre O, PA and PB are tangents to the circle at point A and Point B, respectively. C is a point on the major arc AB. If ∠ACB = 50°, then find the measure of ∠APB.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 80°
Given:
PA and PB are tangents to the circle at point A and Point B
C is a point on the major arc AB
∠ACB = 50°
Calculations:
∠AOB = 2 × ∠ACB (angle subtended by an arc at the centre is twice the angle subtended by it at any part of the circle)
∠AOB = 2 × 50 = 100
Now, take AOBP as a quadrilateral
⇒ ∠A + ∠AOB + ∠B + ∠P = 360
⇒ 90 + 100 + 90 + ∠P = 360
⇒ ∠P = 80°
Hence, the measure of ∠APB is 80°.