RU-ALLRUSSIAN 1963 Problem 3
(a) The two diagonals of a quadrilateral each divide it into two parts of equal area. Prove it is a parallelogram.
(b) The three main diagonals of a hexagon each divide it into two parts of equal area. Prove they have a common point. [If ABCDEF is a hexagon, then the main diagonals are AD, BE and CF.]
Dataset text NuminaMath olympiads. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.