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 `3` (b) 2 (c) `3/2` (d) 1

Explanation

To solve the problem, we need to find the radius of the inscribed circle in the quadrilateral ABCD, given the area, the relationships between the sides, and the perpendicularity conditions. Here’s a step-by-step solution:

### Step 1: Define the sides of the quadrilateral
Let:
- \( AB = 2x \) (since \( AB \) is twice \( CD \))
- \( CD = x \)
- \( AD = h \) (the height, since \( AD \) is perpendicular to both \( AB \) and \( CD \))

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