Geometry Problem 981. Triangle, Concurrent Cevians, Midpoints, Area, Hexagon

AA₁, BB₁, and CC₁ are concurrent cevians of triangle ABC at O (see the infographic below). A₂, B₂, and C₂ are the midpoints of AO, BO, and CO, respectively. If S₁ S₂ and S₃ are the areas of triangle ABC, hexagon A₁C₂B₁A₂C₁B₂, and triangle A₂B₂C₂, prove that S₁ = 2.S₂ = 4.S₃
 

Sketch of problem 981

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Triangles
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