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If the angle between two tangents drawn ...

If the angle between two tangents drawn from an external point P to a circle of radius `a` and center O , is `60^(@),` then find the length of OP.

A

`2a`

B

`4a`

C

`6a`

D

`8a`

Text Solution

Verified by Experts

The correct Answer is:
A
PA and PB are two tangents from an external point P such that
` " "angleAPB=60^(@)`
`:." "angleOPA=angleOPB=30^(@)`
(`because` tangents are equally inclined at the centre)
Also,`" "angleOAP=90^(@)" "`(radius through point of contact is perpendicular to the tangent)

Now in right `DeltaOAP ,`
`sin30^(@)=(OA)/(OP)`
`implies" "(1)/(2)=(a)/(OP)" "implies" "OP=2a` units
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