In fig 2, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touchesthe sides - Maths - Circles

Question

In fig 2, a circle with centre O is inscribed in a quadrilateral
ABCD such that, it touchesthe sides BC, AB, AD and CD at points P,
Q, R and S respectively If AB=29cm, AD=23,B= 90 and DS=5cm, then
the radius of the circle (in cm ) is:

Somnath maths · Accepted Answer

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Given,AB=29cm,AD=23cm, B=900,DS=5cm Join OP and OQ Then,OP=OQ,
OP⊥PB OQ⊥BQ ∴OPBQ is a square Tangles from an
external point,being equal,we have: DS=DR, BP=QB,
AS=AP∴DS=DR=5cm∴AS=18cm [23−5] also AP=18cm
PB=AB−AP =29−18 =11cm ∴OQ=11cm The radius is
11cm

In fig. 2, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touchesthe sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB=29cm, AD=23,B= 90 and DS=5cm, then the radius of the circle (in cm.) is: