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Geometric inequality with areas of a hexagon and triangle

Source: XIII Rioplatense Mathematical Olympiad (2004), Level 3

July 26, 2011
inequalitiesgeometrycircumcircleinradiusgeometry unsolved

Problem Statement

In a convex hexagon ABCDEFABCDEF, triangles ACEACE and BDFBDF have the same circumradius RR. If triangle ACEACE has inradius rr, prove that Area(ABCDEF)≤Rr⋅Area(ACE). \text{Area}(ABCDEF)\le\frac{R}{r}\cdot\text{Area}(ACE).
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