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Find the dimensions of the rectangle with maximum area that can be inscribed in a circle of radius 10.

I start by drawing the diagram and it seems to me like the circle radius corresponds with a line from the center of the rectangle to one of the rectangle points on the edge of the circle. This could give me a triangle with pythagorean theorem. I should find the value of x that yields largest area as my priority, after that I can find y easily.

Latex is not behaving today so i'll try my best without. y/2 = (10^2-(x/2)^2)^(1/2)

Area of a square is xy, duh.

Plugging this in gives me a chain rule problem which ultimately comes out with the critical points 0, -10 and 10, all of which yield 0 Area (obviously), there has to be a critical point that I am missing between 0 and 10 but the derivative of A(x) doesn't yield any.

I'm stumped.