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To draw a pair of tangents to a circle w...

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^(@)`

Text Solution

Verified by Experts

The correct Answer is:
D
(D) 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 ponits of those two radii ( at which tangent are drawn ) and the centre of the circles is a quadrilateral.

From figure it is quadrilateral,
`anglePOQ+anglePRQ=180^(@)` [`:.` sum of opposite angles are `180^(@)`]
`60^(@)+ theta=180^(@)`
`:. theta=120`
Hence, the required angle between them is `120^(@)`.
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