Answer
$r = \frac{2 \sqrt{s(s-a)(s-b)(s-c)}}{a+b+c}$
Work Step by Step
First of all, we know Heron's formula:
$A = \sqrt{s(s-a)(s-b)(s-c)}$
We also know that area is given by:
$A = 1/2rP = 1/2(r)(a+b+c)$
Setting these equal gives:
$1/2(r)(a+b+c) = \sqrt{s(s-a)(s-b)(s-c)} \\r = \frac{2 \sqrt{s(s-a)(s-b)(s-c)}}{a+b+c} $
