Problem 559: Triangle, Cevian, Incenters, Angle, 90 Degrees.
Level: High School, College, Math Education The figure shows a triangle ABC with a cevian BD. If E is the incenter
of triangle ABD and F the incenter of triangle BCD, prove that the
measure of angle EDF is 90 degrees.
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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