Relations between Some Triangles Associated with Excircles

Let ABC be a triangle with incenter I. Let the excircles opposite A, B, and C be tangent to the extensions of the sides of ABC at the points D, E, F, G, H, and J. Then area(HAI) = area(ECI), area(JBI) = area(FCI), and area(DBI) = area(GAI).

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The statement of the theorem is in Problem 113. Area of Triangles, Incircle, Excircles.
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