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In the given figure, a circle is inscribed in a quadrilateral `ABCD` touching its sides `AB`, `BC`, `CD` and `AD` at `P,Q,R` and `S` respectively. If the radius of the circle is `10cm`, `BC=38cm`, `PB=27cm` and `ADbotCD` then the length of `CD` is

A

`11cm`

B

`15cm`

C

`20cm`

D

`21cm`

Text Solution

Verified by Experts

`BQ=PB=27cm`, `CQ=BC-BQ=(38-27)cm=11cm`, `CR=CQ=11cm`.
Join `OR`, Then, `SDRO` is a square.
And so, `CD=DR+CR=(10+11)cm=21cm`.
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RS AGGARWAL-CIRCLES-Multiple-choice questions (MCQ)
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