Geometry Problem 1390: Triangle, any point, perpendicular, sum of the
squares, Tutoring

Proposition

The figure below shows a triangle ABC and a point P. PD, PE and PF are
perpendicular to AB, BC, and AC, respectively. Prove that AD^{2} + BE^{2} + CF^{2} =
BD^{2} + EC^{2} + FA^{2}.