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In figure, AT is a tangent to the circle...

In figure, AT is a tangent to the circle with centre 0 such that OT = 4 cm and `angleOTA=30^(@)`. Then, AT is equal to

A

4 cm

B

2 cm

C

`2sqrt3cm`

D

`4sqrt3cm`

Text Solution

Verified by Experts

The correct Answer is:
C
Join OA.
We know that, the tangent at any point of a circle is perpendicular to the radius through the piont of contact.
`:.angleOAT=90^(@)`
In `DeltaOAT,` `cos30^(@)=(AT)/(OT)`
`rArr(sqrt3)/(2)=(AT)/(4)`
`rArrAT=2sqrt3cm`
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