IMO Shortlist 1983 problem 3


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2. travnja 2012.
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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.
Izvor: Međunarodna matematička olimpijada, shortlist 1983