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A circle is drawn in a sector of a large...

A circle is drawn in a sector of a larger circle of radius `r ,` as shown in figure. The smaller circle is tangent to the two bounding radii and the arc of the sector. The radius of the smaller circle is `r/2` (b) `r/3` (c) `(2sqrt(3)r)/5` (d) `r/(sqrt(2))`

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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