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 illstructured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

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