Question

If a chord AB subtends an angle of 60° at the centre of a circle, then the angle between the tangents to the circle drawn from A and B is ______.

विकल्प

• 30°

• 60°

• 90°

• 120°

Answer 1

If a chord AB subtends an angle of 60° at the centre of a circle, then the angle between the tangents to the circle drawn from A and B is 120°.

Explanation:

Let P be the point of intersection of tangents at A and B.

Then, OAPB is a cyclic quadrilateral.

∴ ∠AOB + ∠AРB = 180°

⇒ ∠APB = 180° – 60°

⇒ ∠APB = 120°