Question
In the given figure, a circle is inscribed in a quadrilateral $ABCD$ in which $\angle\text{B}=90^{\circ}.$ It $AD = 23\ cm, AB = 29\ cm$ and $DS = 5\ cm,$ find the radius $r$ of the circle.
✓
Answer
In the figure, $O$ is the centre of the circle inscribed in a quadrilateral $ABCD$ and $\angle\text{B}=90^{\circ} AD = 23\ cm, AB = 29\ cm, DS = 5\ cm.$
$OP = OQ ($radii of the same circle$)$
$AB$ and $BC$ are tangents to the circle and $OP$ and $OQ$ are radii
$OP ⊥ BC$ and $OQ ⊥ AB$
$\angle\text{OPB}=\angle\text{OQB}=90^{\circ}$
$PBQO$ is a square
$DS$ and $DR$ are tangents to the circle
$DR = DS = 5\ cm$
$AR = AD – DR = 23 – 5 = 18\ cm$
$AR$ and $AQ$ are the tangents to the circle
$AQ = AR = 18\ cm$ But $AB = 29\ cm$
$OP = OQ ($radii of the same circle$)$
$AB$ and $BC$ are tangents to the circle and $OP$ and $OQ$ are radii
$OP ⊥ BC$ and $OQ ⊥ AB$
$\angle\text{OPB}=\angle\text{OQB}=90^{\circ}$
$PBQO$ is a square
$DS$ and $DR$ are tangents to the circle
$DR = DS = 5\ cm$
$AR = AD – DR = 23 – 5 = 18\ cm$
$AR$ and $AQ$ are the tangents to the circle
$AQ = AR = 18\ cm$ But $AB = 29\ cm$
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