Problem 273: Triangle, Perpendiculars, Area of Squares
In the figure below, from a point O inside or outside of a triangle ABC, perpendiculars are drawn to the sides meeting AB, BC, and AC , at points D, E, and F, respectively. If S_{1}, S_{2}, S_{3}, S_{4}, S_{5}, and S_{6} are the areas of the squares of sides AD, DB, BE, EC, CF, and FA, respectively, prove that S_{1} +S_{3} + S_{5} = S_{2} + S_{4} + S_{6}.

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