IMO Shortlist 1989 problem 28


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Dodao/la: arhiva
2. travnja 2012.
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Consider in a plane P the points O,A_1,A_2,A_3,A_4 such that \sigma(OA_iA_j) \geq 1 \quad \forall i, j = 1, 2, 3, 4, i \neq j. where \sigma(OA_iA_j) is the area of triangle OA_iA_j. Prove that there exists at least one pair i_0, j_0 \in \{1, 2, 3, 4\} such that \sigma(OA_iA_j) \geq \sqrt{2}.
Izvor: Međunarodna matematička olimpijada, shortlist 1989