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