Problem

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Tags: geometry



Let $XY Z$ be a triangle. The convex hexagon $ABCDEF$ is such that $AB; CD$ and $EF$ are parallel and equal to $XY; Y Z$ and $ZX$, respectively. Prove that area of triangle with vertices at the midpoints of $BC; DE$ and $FA$ is no less than area of triangle $XY Z.$ (8 points)