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.