Online Geometry Problem 121: Triangle, Median, Similarity and Area. Level: High School, College,
In the figure below, given a triangle
ABC of area S, the medians BM and CN meet at G. Let be BD = 2 CD, the cevian AD meets BM and CN at E and F respectively.
Area of triangle EFG is S1. Prove that:
GE/EM = 2/3, GF/CF = 1/3 and
S1 = S/60.