I've been brushing up on my math skills and found there's a neat way to find two things you probably been told to do in math at one point: find the radius of a circle that would fit neatly around a square or find the square that would fitly around the circle.
Starting with this rule first thing you should note is the diagonal lines cutting through the square is the diameter of the circle
So with that your done since if you take a half of the square you'll get a right angled triangle and with the equation: a2 + b2 = c2 you can use the width of the square which are equal (a & b) do the math and you'll get the diameter of the circle.
This way you can find the diameter of the circle using the details of the square only.
You can also rotate the square 45% and get this
and using this as a rule that you only know the circle's diameter or radius determine the width of the square
using the same rules only from a different angle so r2 + r2 = w2
If you wanted you can just look at the square itself and using the same rule
find the circle's radius.