Question

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 quadrilaterals ABCD touching all the sides, then its radius is

(a) 3

(b) 2

(c) 3/2

(d) 1

Answer 1

Correct option is (b) 2

Given that AB = 2CD 

Let CD = a 

\(\therefore\) AB = 2a 

\(\therefore\) B(2a, 0) 

and c(a,2r) 

Let the centre of in circle be (r, r)

Where r is the radius of the circle