Online Geometry Problems

Online Geometry Problem 128: Incenter of a Triangle, Angle Bisectors, Sum of Ratios. Level: High School, SAT Prep, College, Mathematics Education

In the figure below, given a triangle ABC and the angle bisectors AD, BE, and CF that meet at the incenter I. Prove that: Formula to prove. View or post a solution.

Triangle, Incenter, Angle bisectors, Sum of Proportion
 

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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