In the figure below, given a triangle
ABC of area S. Let be S_{1} the area of the
central star determined by the triangles DFH and EGM. D, E, F,
G, H, and M are determined by trisection of each
side of the triangle ABC and connecting the corresponding points
A', A", B', B", C', and C" with the opposite vertex.
Prove that
.
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