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On the Areas of Triangles Associated with an Excircle

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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 (March 2011)
After work by: Antonio Gutierrez
Open content licensed under CC BY-NC-SA

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

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