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On the Areas of Triangles Associated with an Excircle


	Let ABC be a triangle. Let D and E be the points of contact of the extensions of AB and AC with the excircle opposite A. Let I be the incenter of ABC. let G and F be the intersections of DI and EI with BC. Let , , and be the areas of GIF, DBG, and ECF, respectively. Then .


	Contributed by: Jay Warendorff After work by: Antonio Gutierrez

The statement of the theorem is in Problem 119. Area of Triangles, Incenter, Excircle.

Excircles (Wolfram MathWorld)

Incircle (Wolfram MathWorld)

"On the Areas of Triangles Associated with an Excircle" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/OnTheAreasOfTrianglesAssociatedWithAnExcircle/

Contributed by: Jay Warendorff

After work by: Antonio Gutierrez

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