KöMaL 2021 A806

Four distinct lines are given in the plane, which are not concurrent and no three of which are parallel. Prove that it is possible to find four points in the plane, $A$, $B$, $C$ and $D$ with the following properties: $(i)$ $A$, $B$, $C$ and $D$ are collinear in this order; $(ii)$ $AB=BC=CD$; $(iii)$ with an appropriate order of the four given lines $A$ is on the first, $B$ is on the second, $C$ is on the third and $D$ is on the fourth line.