Question
In the given figure, a circle is inscribed in a quadrilateral ABCD in which $\angle\text{B}=90^{\circ}.$ It AD = 23cm, AB = 29cm and DS = 5cm, 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 = 23cm, AB = 29cm, DS = 5cm.
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 = 5cm
AR = AD – DR = 23 – 5 = 18cm
AR and AQ are the tangents to the circle
AQ = AR = 18cm But AB = 29cm
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 = 5cm
AR = AD – DR = 23 – 5 = 18cm
AR and AQ are the tangents to the circle
AQ = AR = 18cm But AB = 29cm
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