Question

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

Options

• True

• False

Answer 1

This statement is False.

Explanation:

Consider the given figure.

In which we have a circle with centre O and AB a chord with ∠AOB = 60°

Since, tangent to any point on the circle is perpendicular to the radius through point of contact,

We get,

OA ⊥ AC and OB ⊥ CB

∠OBC = ∠OAC = 90°  ...[Equation (1)]

Using angle sum property of quadrilateral in Quadrilateral AOBC,

We get,

∠OBC + ∠OAC + ∠AOB + ∠ACB = 360°

90° + 90° + 60° + ∠ACB = 360°

∠ACB = 120°

Hence, the angle between two tangents is 120°.