Geometry Problems, Online Education

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 Sa, Sb, and Sc are the areas of the squares built on the sides, prove that  Sa + Sb + Sc = 2(AB.AF + BC.BD + AC.CE).
 

Triangle with squares, Area, Altitude
 

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