  Given a real cubic function $f(x)$ with three roots, take an equilateral
triangle $ABC$, the projections of which vertices are the roots of $f(x)$.
There is a folklore fact that the vertical lines through the extrema of $f(x)$
are tangent to the inscribed circle of $ABC$. We generalise this fact to a
regular $n$-gon and the corresponding degree $n$ polynomial.
