In triangle ABC, points D and E are on sides BC and CA respectively, and points F and G are on side AB with G between F and B. BE intersects CF at point O_1 and BE intersects DG at point O_2. If FG = 1, AE = AF = DB = DC = 2, and BG = CE = 3, compute $\tfrac{O_1O_2}{BE}$.
I couldn't think of other method to solve this(besides, iI don't know mass point geometry) will choose the most reasonable answer!
Answer is in problem 3 in this article: http://en.wikipedia.org/wiki/Mass_point_geometry
Thanks in advance.