decomposition by two long diagonals of a hexagon, circumcircle exists
Source: 41st Austrian Mathematical Olympiad National Competition (Final Round, part 2) 3rd June 2010 p6
September 5, 2019
geometrycircumcirclehexagoncombinatorial geometry
Problem Statement
A diagonal of a convex hexagon is called long if it decomposes the hexagon into two quadrangles.
Each pair of long diagonals decomposes the hexagon into two triangles and two quadrangles.
Given is a hexagon with the property, that for each decomposition by two long diagonals the resulting triangles are both isosceles with the side of the hexagon as base.
Show that the hexagon has a circumcircle.