Geometry Problem 1153: Triangle, Angle Bisectors, Perpendicular, Congruence. Level: School, College, Mathematics Education

The figure below shows a triangle ABC (AB > BC). AD is the bisector of angle A and CE bisector of angle C. ED and AC extended meet at F. If FG and FH are perpendicular to BC and AB, respectively, prove that FG = FH.
 
 

See also:
Isolines of problem 1153.
GeoGebra of problem 1153