Online Geometry Problem 775: Triangle, Isogonal lines, Congruent angles,
Perpendicular, Metric Relations. Level: High School, College,
Mathematics Education

The figure below shows a triangle ABC with
angle ABD = angle EBC. DF and EH are perpendicular to AB, DG and EM are
perpendicular to BC. If DF = 8, DG = 28, EH = 25, find EM.