Question

Let ABCD be a quadrilateral with area 18, with side AB parallel to CD and AB = 2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is

• A. 3
• B. 2
• C.
• D. 1

Answer 1

The correct option is B

2

Area of the quadrilateral $=\frac{1}{2}(x+2x)2r$

$3xr=18$

$xr=6$

CD = x

AB = 2x

OP = OM = PQ = OQ = AM = r

$tan\theta =\frac{OP}{PC}$

$=\frac{r}{x-r}\dots \dots \left(1\right)$

In $\Delta OBM$

$tan\theta =\frac{2x-r}{r}\dots \dots \left(2\right)$

From (1) and (2) we get,

$x=\frac{3r}{2}$

$\therefore$ r = 2.