  A polynomial system with $n$ equations in $n$ variables supported on a set
$\mathcal{W}\subset\mathbb{R}^n$ of $n+2$ points has at most $n+1$
non-degenerate positive solutions. Moreover, if this bound is reached, then
$\mathcal{W}$ is minimally affinely dependent, in other words, it is a circuit
in $\mathbb{R}^n$. For any positive integer number $n$, we determine all
circuits $\mathcal{W}\subset\mathbb{R}^n$ which can support a polynomial system
with $n+1$ non-degenerate positive solutions. Restrictions on such circuits
$\mathcal{W}$ are obtained using Grothendieck's real dessins d'enfant, while
polynomial systems with $n+1$ non-degenerate positive solutions are constructed
using Viro's combinatorial patchworking.
