Let
be an equilateral triangle and
the set of all points contained in the three segments
,
, and
(including
,
, and
). Determine whether, for every partition of
into two disjoint subsets, at least one of the two subsets contains the vertices of a right-angled triangle.
%V0
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.
Školjka