diagonal in convex hexagon cuts off area <=1/6 area of hexagon
Source: IV All-Ukrainian Tournament of Young Mathematicians, Qualifying p8
May 19, 2021
geometrygeometric inequalityhexagonconvexdiagonalareaUkrainian TYM
Problem Statement
Prove that in an arbitrary convex hexagon there is a diagonal that cuts off from it a triangle whose area does not exceed of the area of the hexagon. What are the properties of a convex hexagon, each diagonal of which is cut off from it is a triangle whose area is not less than the area of the hexagon?