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

Explanation

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

### Step 1: Understand the Problem
We have a circle with radius \( A \) and we want to inscribe a rectangle within this circle. The goal is to determine the dimensions of the rectangle that yield the maximum area.

### Step 2: Set Up the Geometry
Let the rectangle have dimensions \( 2x \) and \( 2y \). The area \( A \) of the rectangle can be expressed as:
\[
...