Online Geometry Problem 815: Triangle, Incircle, Semicircles, Arbelos,
Area. Level: High School,
SAT Prep, College,
The figure below shows a triangle
ABC with the incircle O of area S, tangent to the sides at D, E, and F.
Sa, Sb, and Sc are the areas of the arbelos bounded by the semicircles of diameter
AB, BC, AC, AD, AF, BD, BE, CE, and CF. Prove that