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
Snapshots
Details
The statement of the theorem is in Problem 119. Area of Triangles, Incenter, Excircle.
Permanent Citation
"On the Areas of Triangles Associated with an Excircle"
http://demonstrations.wolfram.com/OnTheAreasOfTrianglesAssociatedWithAnExcircle/
Wolfram Demonstrations Project
Published: March 7 2011