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Geometry Problem 479: Triangle, Cevians, Concurrency, Transversal, Proportion

The figure shows a non-isosceles triangle ABC, the cevians AE, BF, and CD are concurrent at O. Line DE cuts BF and AC extended at H and G, respectively. Prove that Formula to prove
 
 

Triangle, Cevian, Concurrency, Transversal, Proportion