In a quadrilateral ABCD, it is given that `AB |\|CD` and the diagonals `AC and BD` are perpendicular to each other. Show that `AD.BC >= AB. CD`.

Explanation

To prove that \( AD \cdot BC \geq AB \cdot CD \) in the given quadrilateral \( ABCD \) where \( AB \parallel CD \) and the diagonals \( AC \) and \( BD \) are perpendicular, we can follow these steps:

### Step 1: Set up the coordinate system
Let the quadrilateral \( ABCD \) be positioned in a coordinate system such that:
- Point \( A \) is at the origin \( (0, 0) \).
- Point \( B \) is at \( (b, 0) \) (since \( AB \) is horizontal).
- Point \( C \) is at \( (c, h) \) where \( h \) is the height above the x-axis.
- Point \( D \) is at \( (d, h) \) (since \( CD \) is parallel to \( AB \)).
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