DE-BUNDESWETTBEWERB 2014 Problem 3

A regular hexagon with side length $1$ is given. Using a ruler construct points in such a way that among the given and constructed points there are two such points that the distance between them is $\sqrt7$ .

Notes: ''Using a ruler construct points $\ldots$ '' means: Newly constructed points arise only as the intersection of straight lines connecting two points that are given or already constructed. In particular, no length can be measured by the ruler.