MathDB
3 concurrent diagonals

Source: Austrian MO 2005 round 1

June 27, 2005
geometryparallelogramgeometric transformationhomothetyreflectiongeometry solved

Problem Statement

We're given two congruent, equilateral triangles ABCABC and PQRPQR with parallel sides, but one has one vertex pointing up and the other one has the vertex pointing down. One is placed above the other so that the area of intersection is a hexagon A1A2A3A4A5A6A_1A_2A_3A_4A_5A_6 (labelled counterclockwise). Prove that A1A4A_1A_4, A2A5A_2A_5 and A3A6A_3A_6 are concurrent.