Geometry Problems, Online Education

 Problem 115. Area of Triangles, Excircles. Level: High School, SAT Prep, College

In the figure below, given a triangle ABC of area S, construct the excircles with excenters P, Q, and R. Let be D, E, F, G, H, and M the tangent points of triangle ABC with its excircles. If S1, S2, S3, S4, S5, and S6 are the areas of the triangles AMR, BFR, BEP, CHP, CGQ, and ADQ respectively, prove that S1 = S2 = S3 = S4 = S5 = S6 = S/2. View or post a solution.

Elearning 115: Triangle Area, Excircles 



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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