In the figure below, given a triangle
ABC and the angle bisectors AD, BE, and CF that meet at the
incenter I. Prove that:
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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."