Geometry Problems, Online Education
Online Geometry Problem 861: Triangle, Incircle, Parallel, Tangent, Metric Relations. Level: High School, College, Mathematics Education

The figure below shows a triangle ABC with the incircle O tangent to AB, BC, and AC at E, F, and D, respectively. GH is parallel to AC and tangent to the circle O.If AE = 7, EG = 1, and FH = 2, find CF.

 

Triangle, Incircle, Tangent, Parallel, Metric Relations
 


 

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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