IMO Shortlist 1978 problem 4


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2. travnja 2012.
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Let T_1 be a triangle having a, b, c as lengths of its sides and let T_2 be another triangle having u, v,w as lengths of its sides. If P,Q are the areas of the two triangles, prove that
16PQ \leq a^2(-u^2 + v^2 + w^2) + b^2(u^2 - v^2 + w^2) + c^2(u^2 + v^2 - w^2).
When does equality hold?
Izvor: Međunarodna matematička olimpijada, shortlist 1978