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

In the given figure, `AT` is a tangent to the circle with centre `O` such that `OT=4cm` and `/_OTA=30^(@)`. Then `AT=?`

A

`4cm`

B

`2cm`

C

`2sqrt(3)cm`

D

`4sqrt(3)cm`

Text Solution

Verified by Experts

In right `DeltaOAT` (having right angle at `A`), we have
`cos(/_OTA)=(AT)/(OT)impliescos30^(@)=(AT)/(4)impliesAT=((sqrt(3))/(2)xx4)cm=2sqrt(3)cm`.
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