JEE Mains Model Paper 25

Let CD = a, then AB = 2a and r be the radius of the circle, then AD = 2r. Let A be the orignand AB and AD as x-axis and y -axis respectively. Teh coordinates fo A, B, C, D arerespectively
(0,0) (2a,0) (a,2r) (0,2r)
Area (ABCD) = (1/2) (a + 2a) (2r) = 18
⇒ ar = 6
Equation of BC is
2rx + ay - 4ar = 0 and the coordinates of the centre of the circle are (r, r)

Since the circle touches BC,

2r2+ar−4ar

√4r2+a2

= r
⇒ 4r4 - 72x2 + 324 = 4r4 + 36
⇒ r = 2