Online Geometry Problem 125: Area of Triangle, Star, Trisection of sides. Level: High School, SAT Prep, College, Mathematics Education

In the figure below, given a triangle ABC of area S. Let be S₁ 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 . View or post a solution