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Hexagon

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December 5, 2010
trigonometrygeometry

Problem Statement

Let ABCDEFABCDEF be a convex hexagon in which diagonals AD,BE,CFAD, BE, CF are concurrent at OO. Suppose [OAF][OAF] is geometric mean of [OAB][OAB] and [OEF][OEF] and [OBC][OBC] is geometric mean of [OAB][OAB] and [OCD][OCD]. Prove that [OED][OED] is the geometric mean of [OCD][OCD] and [OEF][OEF]. (Here [XYZ][XYZ] denotes are of △XYZ\triangle XYZ)
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