Question 16
Let $ABC$ be an equilateral triangle, and $\mathcal{E}$ the set of all points contained in the three segments $AB$, $BC$ and $CA$ (with $A$, $B$ and $C$ included). Determine if it is true that for each partition of $\mathcal{E}$ into two disjoint sets, at least one of the two sets contains the vertices of a right triangle. justify the answer.