Radius of circumference tangent to square and circular sector I would like to find the radius of the circumference shown in figure, knowing the side of the square is 5. 
I have decided to note said radius $r$ and the tiny diagonal bit not included in any circle as $y$.
I think one way to solve this is to find a system composed of two equations and then to solve for $r$ and $y$.
However, the only equation I was able to find so far is $$5\sqrt{2}=5+2r+y.$$
How can I find another equation? Or is there a better way to solve this?

Note that $r+y=\sqrt{2}r$. This can be seen by placing a dot at the centre $C$ of the little circle, and noting that the line segment joining $C$ to the bottom left corner is the diagonal of an $r\times r$ square. 
More briefly, $5\sqrt{2}=5+r+\sqrt{2}r$. 
