jmc

The radius $r$ of a circle inscribed within three mutually externally tangent circles of radii $a$, $b$ and $c$ is given by $$\frac{1}{r}=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+2\sqrt{\frac{1}{ab}+\frac{1}{ac}+\frac{1}{bc}}.$$What is the value of $r$ when $a=4$, $b=9$ and $c=36$?