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 Problem 120. Area of Triangles, Incenter, Excircles. Level: High School, SAT Prep, College

In the figure below, given a triangle ABC, construct the incenter I and the excircles. Let be D, E, F, G, H, and J the tangent points of triangle ABC with its excircles. K, M, N, P, Q, and R are the intersection points of triangle ABC and ID, IE, IF, IG, IH, and IJ respectively. If S1, S2, S3, S4, S5, S6, S7, S8, and S9, are the areas of the shaded triangles, prove that S1+S2+S3+S4+S5+S6 = S7+S8+S9.
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Elearning 119: Triangle area

 

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."

 

 

Problem 120: Triangle area. Elearning.

 

 
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Last updated: June 16, 2008