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

To solve the problem, we need to find the radius \( R \) of the circle inscribed in the quadrilateral \( ABCD \) given the area and the relationships between the sides.

### Step-by-Step Solution:

1. **Understanding the Quadrilateral**:
- We know that \( AB \) is parallel to \( CD \) and \( AB = 2CD \).
- Let \( CD = L \), then \( AB = 2L \).
- Let \( AD \) be the height from \( AB \) to \( CD \). Since \( AD \) is perpendicular to both \( AB \) and \( CD \), we can denote the height as \( h \).
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