CircleHard

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 quadrilateral ABCD touching all the sides, then its radius is

Options

A.3
B.2
C.3/2
D.1

Solution

           
18 = (3α)(2r)     ⇒ αr = 6
Line y = - (x - 2α) is tangent to (x - r)2 + (y - r)2 = r2
2α = 3r and αr = 6
r = 2.

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