KVPY SA Exam 2012 Question Paper

Question : 8 of 80

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A circle is drawn in a sector of a larger circle of radius r, as shown in the adjacent figure. The smaller circle is tangent to the two bounding radii and the arc of the sector. The radius of the small circle is

$r/2$
$r/3$
${2√3r}/5$
$r/√2$

Validate

Solution:

Say the radius of smaller circle is x
Here OP = x cosec 30º
while OQ = r = x + x cosec 30º

x=r/3

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