Let $m$ and $n$ be integers. If $K_1$ is a circle of radius $1/m^2$

and $K_2$ is a circle of radius $1/n^2$, and if $K_1$, and $K_2$,

are tangent to each other and both are tangent to the same line,

find the radius of the circle tangent to both $K_1$ and $K_2$ and

to the line that lies in the area enclosed by them.