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Relations between Some Triangles Associated with Excircles


	Let ABC be a triangle with incenter I. Let the excircles opposite A, B, and C be tangent to the extensions of the sides of ABC at the points D, E, F, G, H, and J. Then area(HAI) = area(ECI), area(JBI) = area(FCI), and area(DBI) = area(GAI).


	Contributed by: Jay Warendorff After work by: Antonio Gutierrez

The statement of the theorem is in Problem 113. Area of Triangles, Incircle, Excircles.

Excircles (Wolfram MathWorld)

Incircle (Wolfram MathWorld)

"Relations between Some Triangles Associated with Excircles" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/RelationsBetweenSomeTrianglesAssociatedWithExcircles/

Contributed by: Jay Warendorff

After work by: Antonio Gutierrez

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