Online Geometry Problem 785: Equilateral Triangle, Parallel to a side,
Perpendicular to a side, Metric relations. Level: High School,
SAT Prep, College,
Mathematics Education

The figure below shows an equilateral triangle ABC with
DE parallel to BC and EF parallel to AB. D and G are on AB; F and H are
on BC. GM and HN are perpendicular to AC. If AC = a, DG = d, FH = f, and
MN = x prove that .