Problem 340. Triangle, Angle Bisectors, Perpendiculars, Exterior Point, Distances. Level: High School, College, SAT Prep.
The figure shows a triangle ABC with
the angle bisectors AD and CE. F is a point on the extension of DE and FG, FH,
and FM are perpendiculars to AB, BC and AC, respectively. Prove
that FH - FG = FM.