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In the figure below, given a triangle
ABC, construct the incenter I and the excircles with
excenters P and Q. Let be D and E the tangent
points of triangle ABC with its excircles. IE and BC meet at H,
and ID and AB meet at G. If S1, S2, S3,
and S4 are the areas of the triangles AIG, BEH, BDG, and
CHI
respectively, prove that S1 + S2 = S3
+ S4.
Post a comment or solution.
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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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