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Q.

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 twobounding radii and the arc of the sector. The radius of the smaller circle is

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a

r2

b

r3

c

23r5

d

r2

answer is B.

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Detailed Solution

Let the radius of smaller circle be x. Here, and  OP=xcosec⁡30∘⇒OQ=r=x+xcosec⁡30∘x=r3
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