In figure, a circle is inscribed within a quadrilateral ABCD. Given that

BC=38cm, BQ=27cm and DC=25cm and that AD is perpendicular to DC. The radius of the circle is

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10cm

14cm

8cm

12cm

answer is B.

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Detailed Solution

∵ Lengths of tangents drawn from an external point to a circle are equal.
∴BQ=BR=27 cm
Let x be the radius of the circle
∴OP=OS=PD=x
Now,
       CR=BC−BR
               =38−27=11 cm
Now CS=CR=11 cm
[∵ Length of tangents from an external point to a circle are equal]
∴DS=CD−CS
           =25cm−11 cm
           =14 cm
But DS=OP=x=14 cm.
Hence radius =OP=14 cm,
∴, Option 2 is the correct answer.

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