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LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the side CD and AB=2CD .Let AD be perpendicular to AB and CD .If a circle is drawn inside the quadrilateral ABCD touching all the side ,then it's radius is A 3 B 2 C 3/2 D 1?
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**Ref:** https://edurev.in/question/547474/LET-ABCD-be-a-quadrilateral-with-area-18-with-sid

Let CD=x then AB=2CD=2x.Let r be the radius of the circle inscribed in the quadrilateral ABCD.

Given: Area of quadrilateral ABCD=18 and ABis|| to CD.

â‡’ 1/2(x+2x).2r=18

â‡’ 3xr=18

â‡’ xr=6-----(1)

OP=OM=PD=OQ=AM=r

â‡’ PC=xâˆ’randMB=2xâˆ’r

Let âˆ PCO=angleOCQ=Î¸ then from right-angled Î”OPC

From (1) & (4) we get,

xr=6

3rr^2=6

r^2=4

r=2

Hence (b) is the correct answer.

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