IMO 1983 Problem 4

Let $ABC$ be an equilateral triangle and $\mathcal{E}$ the set of all points contained in the three segments $AB$ , $BC$ , and $CA$ (including $A$ , $B$ , and $C$ ). Determine whether, for every partition of $\mathcal{E}$ into two disjoint subsets, at least one of the two subsets contains the vertices of a right-angled triangle.