Let $ABC$ be an equilateral triangle and $P$ any point inside $ABC$. Show that the segments $AP$, $BP$, $CP$ are sides of some triangle $T(P)$ and find $P$ for which the area of $T(P)$ is largest. The problem was solved by Prof. Vladislav Kargin. For a detailed solution see the following link {{:pow:2024fproblem7.pdf|Solution}}.