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Problem 561: Triangle, Cevian, Incenter, Perpendicular, 90 Degrees.
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 OG is perpendicular to AC, prove that the measure of angle EGF is 90 degrees.
 

Triangle, Cevian, Incenter, Tangency point
 


 

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."

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