In the given figure, a circle with centre O, is inscribed in a quadrilateral ABCD such that it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, $∠$ = $90^{o}$ and DS = 5 cm then find the radius of the circle.

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Solution

AB=29cm,
AD=23cm,
∠B=90∘
and
DS=5cm

AQ=AR
DS=DR
CP=CS
PB=BQ
AB=AQ+BQ
Since
DS=5cm
DR=5cm
AR=23−5=18cm
AQ=18cm
and BQ=29−18=11cm
Answer : 11 cm

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In Fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P,Q,R and S respectively, If AB = 29 cm, AD = 23 cm, $D B = 90^{\circ}$ and DS = 5 cm, then the radius of the circle (in cm.) is :

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In the given figure, a circle with centre O, is inscribed in a quadrilateral ABCD such that it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠ = 90o and DS = 5 cm then find the radius of the circle.

AB=29cm, AD=23cm, ∠B=90∘ and DS=5cm AQ=AR DS=DR CP=CS PB=BQ AB=AQ+BQ Since DS=5cm DR=5cm AR=23−5=18cm AQ=18cm and BQ=29−18=11cm Answer : 11 cm

In the given figure, a circle with centre O, is inscribed in a quadrilateral ABCD such that it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, $∠$ = $90^{o}$ and DS = 5 cm then find the radius of the circle.

AB=29cm,
AD=23cm,
∠B=90∘
and
DS=5cm

AQ=AR
DS=DR
CP=CS
PB=BQ
AB=AQ+BQ
Since
DS=5cm
DR=5cm
AR=23−5=18cm
AQ=18cm
and BQ=29−18=11cm
Answer : 11 cm