Given a circle, prove that the square is the rectangle of maximal area that can be inscribed in the circle.

* Proof. * Let and denote the lengths of the sides of the inscribed rectangle, and denote the radius of the circle. Then implies . Therefore,

We then have when and

Hence, has a maximum at . By our equation for we then have

Thus, , so the rectangle is a square

your radius is 2r, instead of r.