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A circle is drawn in a sectore of a larg...

A circle is drawn in a sectore of a larger circle of radius r, as shown in fugure. The smaller circle is tangent to the two bounding radii and the are of the sector. The radius of the smaller circle is

A

`r/2`

B

`r/3`

C

`(2sqrt3r)/5`

D

`r/sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the radius of smaller circle be x. Here,
`OP=xcosec30^@`
`andOQ=r=xcosec30^@`
`rArr =x=r/3`
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