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