Online Geometry
Problem 471. Triangle, Parallel, Side, Concurrency,
Area, Similarity

The figure shows a triangle ABC of
area S. Lines DE, FG, and HM, concurrent at a point O, are
parallel to AC, BC, and AB respectively. If S_{1}, S_{2},
and S_{3} are the areas of triangles ODF, OME, and OGH
respectively, prove that
.