  Heron's formula states that the area $K$ of a triangle with sides $a$, $b$,
and $c$ is given by $$ K=\sqrt {s(s-a) (s-b) (s-c)} $$ where $s$ is the
semiperimeter $(a+b+c)/2$. Brahmagupta, Robbins, Roskies, and Maley generalized
this formula for polygons of up to eight sides inscribed in a circle. In this
paper we derive formulas giving the areas of any $n$-gon, with odd $n$, in
terms of the ordered list of side lengths, if the $n$-gon is circumscribed
about a circle (instead of being inscribed in a circle). Unlike the cyclic
polygon problem, where the order of the sides does not matter, for the
inscribed circle problem (our case) it does matter. The solution is much easier
than for the cyclic polygon problem, but it does generalize easily to all odd
$n$. We also provide necessary and sufficient conditions for there to be
solutions in the case of even $n$.
