MathDB

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

\frac{3 \sqrt{3}}{4(m+2)}

Problem Statement