Problem

Source: ELMO 2003 Problem 1

Tags: inequalities, geometry, trigonometry, geometry unsolved



Let $ABCDEF$ be a convex equilateral hexagon with sides of length $1$. Let $R_1$ be the area of the region contained within both $ACE$ and $BDF$, and let $R_2$ be the area of the region within the hexagon outside both triangles. Prove that: \[ \min \{ [ACE], [BDF] \} + R_2 - R_1 \le \frac{3\sqrt{3}}{4}. \]