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KVPY2012MathematicsCircle

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 -

Options

  1. Ar 2
  2. Br 3
  3. C2 3 r 5
  4. Dr 2

Correct answer

B. r 3

Step-by-step solution

Say the radius of smaller circle is x Here OP = x cosec 30^ while OQ = r = x + x cosec 30^ x = r 3

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