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The infographic below shows a regular hexagon ABCDEF of area S. P is any point and PA, PB, PC,PD, PE, and PF form triangles of areas S_{1}, S_{2}, S_{3}, S_{4}, S_{5}, and S_{6}. Prove that S_{1}+S_{3}+S_{5} = S_{2}+S_{4}+S_{6} = S/2.

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