In the given figure, a circle is inscribed in a quadrilateral $ABCD$ in which $\angle B = 90°$. If $AD = 17$ cm, $AB = 20$ cm and $DS = 3$ cm, then find the radius of the circle.

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Question

In the given figure, a circle is inscribed in a quadrilateral $ABCD$ in which $\angle B = 90°$. If $AD = 17$ cm, $AB = 20$ cm and $DS = 3$ cm, then find the radius of the circle.

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Accepted Answer

Step 1: $DR = DS = 3$ cm
$	herefore AR = AD - DR = 17 - 3 = 14$ cm
Step 2: $\Rightarrow AQ = AR = 14$ cm
$	herefore QB = AB - AQ = 20 - 14 = 6$ cm
Step 3: Since $QB = OP = r$ $	herefore$ radius $= 6$ cm

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