triangles are constructd in exterior of a convex hexagon
Source: 9th-th Hungary-Israel Binational Mathematical Competition 1998
July 13, 2007
geometryparallelogramgeometry proposed
Problem Statement
On the sides of a convex hexagon , equilateral triangles are constructd in its exterior. Prove that the third vertices of these six triangles are vertices of a regular hexagon if and only if the initial hexagon is affine regular. (A hexagon is called affine regular if it is centrally symmetric and any two opposite sides are parallel to the diagonal determine by the remaining two vertices.)