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°

Solution:

It is given that

O is the centre of a circle to which a pair of tangents PQ and PR from the point P touches the circle at Q and R

∠RPQ = 60°

We know that

∠OQP = 90° = ∠ORP

The angle between a tangent to a circle and the radius of the same circle passing through the point of contact is 90°

Using the angle sum property of quadrilaterals

∠OQP + ∠RPQ + ∠ORP + ∠ROQ = 360°

Substituting the values

90° + 60° + 90° + ∠ROQ = 360°

∠ROQ = 120°

Therefore, the angle between them should be 120°.

✦ Try This: To draw a pair of tangents to a circle which are inclined to each other at an angle of 40°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 11

NCERT Exemplar Class 10 Maths Exercise 10.1 Problem 6

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°

Summary:

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°

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