Online Geometry Problem 634: Right Triangle, Altitude, Incenters, Areas. Level: High School, Honors Geometry, College, Mathematics Education

The figure shows a right triangle ABC, AH is the altitude, and D, E and F are the incenters of triangles ABC, AHB, and BHC, respectively. Prove that the sum of the areas of triangles AEB and BFC is equal to the area of triangle ADC.