Problem

Source: Romanian TST 1998

Tags: geometry, geometry proposed



Let $ABC$ be an equilateral triangle and $n\ge 2$ be an integer. Denote by $\mathcal{A}$ the set of $n-1$ straight lines which are parallel to $BC$ and divide the surface $[ABC]$ into $n$ polygons having the same area and denote by $\mathcal{P}$ the set of $n-1$ straight lines parallel to $BC$ which divide the surface $[ABC]$ into $n$ polygons having the same perimeter. Prove that the intersection $\mathcal{A} \cap \mathcal{P}$ is empty. Laurentiu Panaitopol