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[ODC]=[HEA]=[GFB], find all values of C

Source: INMO 2013 P5

February 3, 2013
geometryrectanglegeometry proposed

Problem Statement

In an acute triangle ABC,ABC, let O,G,HO,G,H be its circumcentre, centroid and orthocenter. Let D∈BC,E∈CAD\in BC, E\in CA and OD⊥BC,HE⊥CA.OD\perp BC, HE\perp CA. Let FF be the midpoint of AB.AB. If the triangles ODC,HEA,GFBODC, HEA, GFB have the same area, find all the possible values of ∠C.\angle C.
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