Online Geometry Problem 786: Right Triangle, Altitude, Hypotenuse, Cevian, Perpendicular, Ratio, Metric relations. Level: High School, SAT Prep, College, Mathematics Education

The figure below shows a right triangle ABC with the altitude BH and cevians BD and BE, so that AD = DE = EC. DF is perpendicular to BE and ratio BH / AC = 2 /5. Find ratio DF / BF.