Question 13
A regular hexagon with side-length $1$ is given. Inside the hexagon $m$ points are given so that no three of them are collinear. The hexagon is split into triangles, so that each of the given $m$ points and each vertex of the hexagon is a vertex of one such triangle. The triangles into which the hexagon is split have no common interior point. Prove that, among them, there exists one triangle whose area is not greater than $\frac{3\sqrt{3}}{4(m+2)}$.
