# Fraction of the area of a square occupied by a circle

We have the following picture:

The radius of the larger circle is twice that of the smaller circle. Find an expression for the fraction of the area of the square which is occupied by the two circles.

I know that the area of the 2 circles together is $5 \pi r^2$, but I can't seem to find a way to express the area of the square in terms of $r$. Can I get a hint?

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To express the side length of the square depending on $r$. Go straight from where the square touches one circle to the circle's centre. Then go the the other circle's centre. Then straight to the edge of the square, where it touches the second circle. What's the angle between the line connecting the centres of the circles and the sides of the square? – Daniel Fischer Sep 17 '13 at 18:31
@DanielFischer Thanks. I'm getting $13.5r^2 + \dfrac{18r^2}{\sqrt{2}}$ for the area of the square.. is that even correct? – MacropusRufus Sep 17 '13 at 18:55

Hint: The diagonal of the square is $2r\sqrt{2}+2r+r+r\sqrt{2}$.