Sum of the lengths of the three segments connecting midpoint
Source: Tuymaada 2008, Senior League, Second Day, Problem 8.
July 18, 2008
analytic geometryinequalitiesgeometry unsolvedgeometry
Problem Statement
A convex hexagon is given. Let 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
Author: N. Sedrakyan