Question

To draw a pair of tangents to a circle, which are inclined to each other at an angle of 45°, we have to draw tangents at the end points of those two radii, the angle between which is ______.

Options

• 105°

• 135°

• 140°

• 145°

Answer 1

To draw a pair of tangents to a circle, which are inclined to each other at an angle of 45°, we have to draw tangents at the end points of those two radii, the angle between which is 135°.

Explanation:

Let PA and PB be the desired tangents to a circle with centre O from an exterior point Р.

Then, ∠АРВ = 45°.

BOAP must be a cyclic quadrilateral.

∴ ∠AOB + ∠APB = 180° 

⇒ ∠AOB = 180° – 45° 

⇒ ∠AOB = 135°

So, the angle between the two radii must be 135°.