Problem

Source: Ukrainian Mathematical Olympiad 2024. Day 2, Problem 9.6

Tags: geometry



You are given a convex hexagon with parallel opposite sides. For each pair of opposite sides, a line is drawn parallel to these sides and equidistant from them. Prove that the three lines thus obtained intersect at one point if and only if the lengths of the opposite sides are equal. Proposed by Nazar Serdyuk