Let be the diameter, the center of the circle, the rectangle, with .
Let . Then the area is .
We have .
If the area is maximum, then the squared area is also maximum.
The maximum value of f is , where .
So, , for .
Here is what I was doing until I realized I used the wrong radius.
Sorry if it seems redundant since RedDogs fine answer, but I worked it out earlier and do not want my attempt to go in vain.
Let x and y be the dimensions of the rectangle. Then area is A=xy
Sub into A and we have:
Max area is then
Now, try the same problem with an inscribed trapezoid