IMO Shortlist 1967 problem 4


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2. travnja 2012.
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Suppose medians m_a and m_b of a triangle are orthogonal. Prove that:

a.) Using medians of that triangle it is possible to construct a rectangular triangle.

b.) The following inequality: 5(a^2+b^2-c^2) \geq 8ab, is valid, where a,b and c are side length of the given triangle.
Izvor: Međunarodna matematička olimpijada, shortlist 1967