Let `A B C D` be a quadrilateral with area `18` , side `A B` parallel to the side `C D ,a n dA B=2C D` . Let `A D` be perpendicular to `A Ba n dC D` . If a circle is drawn inside the quadrilateral `A B C D` touching all the sides, then its radius is `a = 3` (b) 2 (c) `3/2` (d) 1

Explanation

With the given details, we can draw the diagram.

Please refer to video to see the diagram.

From the diagram,

In `Delta BEC`,

`BC^2 = BE^2+CE^2`

`=>(a-r+2a-r)^2 = (2r)^2 +a^2`

`=>a = 3/2r`

Now, area of the quadrilateral,

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