PA and PB are two tangents from a point P outside the circle with centre O. If A and B are points on the circle such that ∠APB = 100°, then ∠OAB is equal to :
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 50°
A tangent to a circle forms a right ange with the circle's radius.
∠OAP = ∠OBP = 90°
∠BAP = ∠ABP = 90° - x
In triangle ABP :
∠BAP + ∠ABP + ∠APB = 180°
⇒ 90° - x + 90° - x + 100° = 180°
⇒ 2x = 100°
⇒ x = 50°