IMO Shortlist 1988 problem 27

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Let ABC be an acute-angled triangle. Let L be any line in the plane of the triangle ABC. Denote by u, v, w the lengths of the perpendiculars to L from A, B, C respectively. Prove the inequality u^2\cdot\tan A + v^2\cdot\tan B + w^2\cdot\tan C\geq 2\cdot S, where S is the area of the triangle ABC. Determine the lines L for which equality holds.
Izvor: Međunarodna matematička olimpijada, shortlist 1988