TITLE: Fitting a circle
QUESTION [5 upvotes]: Given a figure like , how can I determine the radius of the circle with middlepoint H analytically? CDFE is a square with sides 6/5, with E and F being points on the circles with radii 2.

REPLY [2 votes]: Maybe using
$$
1^2+(\tfrac 65+r)^2=(2-r)^2
$$
to have
$$
r=\frac{39}{160}
$$

Explanation: Let $r$ denote the readius of the circle in question. Then the coordinates of the point $H$ is $H=(1,\frac 65+r)$, and the direct distance from the origin to $H$ must be $2-r$. Then Pythagoras gives us the above equation.