Another Relation between the Areas of Triangles Associated with an Excircle
Let ABC be a triangle. Let D and E be the points of contact of the incircle of ABC with AB and AC. Let J be the excenter of the excircle opposite A and let G and F be the intersections of DJ and EJ with BC. Let , , and be the areas of GJF, DBG, and ECF, respectively. Then .
The statement of the theorem is in Problem 188. Area of Triangles, Incenter, Excenter.