Problem 280: Quadrilateral, Perpendiculars, Area of Squares
In the figure below, from a point O inside or outside of a quadrilateral ABCD, perpendiculars are drawn to the sides meeting AB, BC, CD, AD at points D, E, F, and G, respectively. If S_{1}, S_{2}, S_{3}, S_{4}, S_{5}, S_{6}, S_{7}, and S_{8} are the areas of the squares of sides AD, DB, BE, EC, CF, FD, DG, and GA, respectively, prove that S_{1} +S_{3} + S_{5} + S_{7} = S_{2} + S_{4} + S_{6} + S_{8} .

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