Question

To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be
(a) 135°
(b) 90°
(c) 60°
(d) 120°

Answer 1

PA and PB are two tangents drawn from P to circle with centre O.

∠APB = 60°

Now,

∠OAP = 90° (Radius is perpendicular to the tangent at the point of contact)

∠OBP = 90° (Radius is perpendicular to the tangent at the point of contact)

In quadrilateral OAPB,

∠AOB + ∠OAP + ∠OBP + ∠APB = 360º (Angle sum property of quadrilateral)

⇒ ∠AOB + 90º + 90º + 60º = 360º

⇒ ∠AOB = 360º − 240º = 120º

Thus, in order to draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be 120°.

Hence, the correct answer is option (d).