If two tangents inclinced at an angle `60^@` are drawn to a circle of radius 3 cm, then find the length of each tangent.

Options

A. `(3)/(2)sqrt3cm`
B. 6 cm
C. 3 cm
D. `3sqrt3cm`

Answer

D

Explanation

Let P be an external point and a pair of tangents is drawn from point P and angle between these two tangents is `60^(@)`

Join OA and OP.
Also, OP is a bisector line of `angleAPC`
`:.angleAPO=angleCPO=30^(@)`
Also, `OAbotAP` Tengent at any point of a circle is perpendicular to the radius through the point of contact.
In right angled `DeltaOAP,` `tan30^(@)=(OA)/(AP)=(3)/(AP)`
`rArr(1)/(sqrt3)=(3)/(AP)`
`rArrAP=3sqrt3cm`
Hence, the length of each tangent is `3sqrt3cm`.