Area of Triangle in Terms of Inradius and Exradii

Theorem
Let $\triangle ABC$ be a triangle whose sides are $a$, $b$ and $c$ opposite vertices $A$, $B$ and $C$ respectively.

Then the area $\AA$ of $\triangle ABC$ is given by:
 * $\AA = \sqrt {r \rho_a \rho_b \rho_c}$

where:
 * $r$ is the inradius
 * $\rho_a$, $\rho_b$ and $\rho_c$ are the exradii of $\triangle ABC$ $a$, $b$ and $c$ respectively.

Also see

 * Heron's Formula, to which this is closely related.