# 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 - Mathematics

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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 ______.

• 135°

• 90°

• 60°

• 120°

#### Solution

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°.

Explanation:

The angle between them should be 120° because in that case the figure formed by the intersection point of pair of tangent, the two end points of those-two radii tangents are drawn) and the centre of the circle is a quadrilateral.

∠POQ + ∠PRQ = 180°  ......[∴ Sum of opposite angles are 180°]

60°+ θ = 180°

θ = 120°

Hence, the required angle between them is 120°.

Concept: Construction of Tangents to a Circle
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 10 Construction
Exercise 10.1 | Q 6 | Page 114
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