Problem

Source: Tuymaada 2008, Senior League, Second Day, Problem 8.

Tags: analytic geometry, inequalities, geometry unsolved, geometry



A convex hexagon is given. Let $ s$ be the sum of the lengths of the three segments connecting the midpoints of its opposite sides. Prove that there is a point in the hexagon such that the sum of its distances to the lines containing the sides of the hexagon does not exceed $ s.$ Author: N. Sedrakyan