Answer
$ r = \frac{ab}{a+b+c}$
Work Step by Step
We know that Area equals $1/2bh$, which in this case is $1/2ab$. We know that area also equals $1/2rP$, where P is the perimeter, which in this case equals $a+b+b$. Thus, we find:
$1/2ab = 1/2 (r) (a+b+c) \\ r = \frac{ab}{a+b+c}$