Problem 545: Acute Triangle, Squares, Altitudes, Area. Level: High School, SAT Prep, College

The figure shows an acute triangle ABC with the the altitudes AD, BE, and CF. If S_a, S_b, and S_c are the areas of the squares built on the sides, prove that  S_a + S_b + S_c = 2(AB.AF + BC.BD + AC.CE).