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.
Geometry problem solving
Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."