Problem 560: Triangle, Cevian, Incenter, Incircle, Perpendicular,
Tangent.
Level: High School, College, Math Education The figure shows a triangle ABC with a cevian BD. Points E, F, and O
are the incenters of triangles ABD, BCD, and ABC, respectively. If EM,
OG, and FH are perpendicular to AC, prove that DM = GH.
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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