Question

In the adjoining figure, a circle is inscribed within a quadrilateral $ABCD$. Given that $BC=38cm,BQ=27cm,DC=25cm$ and that $AD$ is perpendicular to $DC$, Find the radius of the circle.

Answer 1

Here, $PD=DS=14cm$

$\angle OPD=\angle PDS=\angle DSO={90}^o$

Hence $\angle POS={90}^o$. Thus the quadrilateral

$OPDS$ is $9$ rectangle. But $PD+DS$

Hence it is a square

Hence, $OP=$ radius $=OS=14cm$