A regular hexagon with side length 1 is given. There are m points in its interior such that no 3 are collinear. The hexagon is divided into triangles (triangulated), such that every point of the m given and every vertex of the hexagon is a vertex of such a triangle. The triangles don't have common interior points. Prove that there exists a triangle with area not greater than 4(m+2)33. geometrycombinatorics proposedcombinatorics