AA_{1}, BB_{1}, and CC_{1} are
concurrent cevians of triangle ABC at O (see the infographic below).
A_{2}, B_{2}, and C_{2} are the
midpoints of AO, BO, and CO, respectively. If S_{1} S_{2} and
S_{3} are the areas of triangle ABC, hexagon A_{1}C_{2}B_{1}A_{2}C_{1}B_{2},
and triangle A_{2}B_{2}C_{2}, prove that
S_{1} = 2.S_{2} = 4.S_{3}
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Sketch of problem 981
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981-990 Triangles
Triangle Area
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Concurrency
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