Geometry Problems, Online Education

 Problem 118. Area of Triangles, Incenter, Excenter. Level: High School, SAT Prep, College

In the figure below, given a triangle ABC, construct the incircle with incenter I and the excircle with excenter E. Let be D and F the tangent points of triangle ABC with its incircle. ED and BC meet at G, and EF and BC meet at H. If S1, S2, and S3 are the areas of the triangles BDG, CFH, and EGH respectively, prove that S1 + S2 = S3. View or post a solution.

Problem 118 

 

 

FACTS AND HINTS:

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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