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).