Geometry Problems, Online Education

 Problem 113. Area of Triangles, Incircle, Excircles. Level: High School, SAT Prep, College

In the figure below, given a triangle ABC, construct the incircle with incenter I and excircles with excenters E1, E2, and E3. Let be D, E, F, G, H, and M the tangent points of triangle ABC with its excircles. If S1, S'1, S2, S'2, S3, and S'3 are the areas of the shaded triangles, prove that S1 = S'1, similarly S2 = S'2, and S3 = S'3. View or post a solution.

Problem 113 Triangle area, incircle, excircle



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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