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 u2·tan A+v2·tan B+w2·tan C≥ 2· S, where S is the area of the triangle ABC. Determine the lines L for which equality holds.