Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.

Explanation

To show that among all rectangles inscribed in a given fixed circle, the square has the maximum area, we can follow these steps:

### Step 1: Understand the Geometry
Let the radius of the circle be \( R \). The rectangle inscribed in the circle will have its vertices on the circumference of the circle.

### Step 2: Set Up the Variables
Let the length of the rectangle be \( L \) and the breadth be \( B \). According to the properties of a circle, the diagonal of the rectangle is equal to the diameter of the circle. Therefore, we have:
\[
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