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If two tangents inclined at an angle of `60^(@)` are drawn to a circle of radius `3cm` then the length of each tangent is

A

`3cm`

B

`(3sqrt(3))/(2)cm`

C

`3sqrt(3)cm`

D

`6cm`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `PQ` and `PR` be the tangents to a circle with centre `O` from a point `P` such that `/_QPR=60^(@)`.
Then, `/_QPO=/_RPO=(1)/(2)/_QPR=30^(@)` [`:'` tangents from an external point are equally inclined to the line joining the point and the centre].
In right `DeltaOPQ`, we have
`tan(/_OPQ)=(OQ)/(PQ)impliestan30^(@)=(3)/(PQ)implies(1)/(sqrt(3))=(3)/(PQ)impliesPQ=3sqrt(3)cm`
Now, `PR=PQ=3sqrt(3)cm`.
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