Difference between revisions of "1983 IMO Problems/Problem 4"
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==Problem== | ==Problem== | ||
Let <math>ABC</math> be an equilateral triangle and <math>\mathcal{E}</math> the set of all points contained in the three segments <math>AB</math>, <math>BC</math> and <math>CA</math> (including <math>A</math>, <math>B</math> and <math>C</math>). Determine whether, for every partition of <math>\mathcal{E}</math> into two disjoint subsets, at least one of the two subsets contains the vertices of a right-angled triangle. Justify your answer. | Let <math>ABC</math> be an equilateral triangle and <math>\mathcal{E}</math> the set of all points contained in the three segments <math>AB</math>, <math>BC</math> and <math>CA</math> (including <math>A</math>, <math>B</math> and <math>C</math>). Determine whether, for every partition of <math>\mathcal{E}</math> into two disjoint subsets, at least one of the two subsets contains the vertices of a right-angled triangle. Justify your answer. | ||
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==Solution== | ==Solution== | ||
Revision as of 17:20, 22 August 2017
Problem
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. Justify your answer.
