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I would appreciate your help on this AMC 2005 question.

A square with side length $2$ and a circle share the same center. The total area of the regions that are inside the circle and outside the square is equal to the area of the regions that are outside the circle and inside the square. What is the radius of the circle?

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    What is the relationship between the region enclosed by the circle and the region enclosed by the square? Think about it. (Hint: If you are trying to find the areas being mentioned in the question, you are making the problem much harder than it needs to be.)2012-11-04

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HINT

The area of the square and circle are equal. Use this to find the radius of the circle.

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    That's not really a hint. I mean, you basically gave away the answer.2012-11-04