Online Geometry Problems

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. See also: Geometric art of problem 634.
 

Right triangle, Altitude, Incenter, Area

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