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Inequality with areas in hexagon

Source: Balkan Mathematical Olympiad 2011. Problem 4.

May 6, 2011
inequalitiesgeometryLaTeXratiotrigonometrygeometry proposed

Problem Statement

Let ABCDEFABCDEF be a convex hexagon of area 11, whose opposite sides are parallel. The lines ABAB, CDCD and EFEF meet in pairs to determine the vertices of a triangle. Similarly, the lines BCBC, DEDE and FAFA meet in pairs to determine the vertices of another triangle. Show that the area of at least one of these two triangles is at least 3/23/2.
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