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.

Let and

The maximum value of f is , where .

So, , for .

Then

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- June 15th 2008, 06:54 AM #1

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- June 15th 2008, 07:18 AM #2

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- June 15th 2008, 08:10 AM #4

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- June 15th 2008, 09:16 AM #5
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**

But

This means

Sub into A and we have:

Max area is then

Now, try the same problem with an inscribed trapezoid