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?

You already have one equation at hand with you.
Now, for the second equation, Assume that you drop a small perpendicular from the centre $C$ of the circle.
So that, $r+y$ is the hypotenuse.
So, $\frac{r}{r+y}=\sin 45^\circ$
Or, $\sqrt2r=r+y$
Or, $y=(\sqrt 2-1)r$
Submit that in the first equation to calculate r.
