area of hexagon by vertices of 2 intersecting tirangles is fixed
Source: TOT 395 1993 Autumn A S3 - Tournament of Towns
June 12, 2024
geometryfixedhexagonequilaterals
Problem Statement
Consider the hexagon which is formed by the vertices of two equilateral triangles (not necessarily equal) when the triangles intersect. Prove that the area of the hexagon is unchanged when one of the triangles is translated (without rotating) relative to the other in such a way that the hexagon continues to be defined.(V Proizvolov)