The figure shows a triangle ABC and the centroid G (point of concurrency of the triangle's medians). If AB = c, BC = a, AC = b, AG = d_a, BG = d_b, and CG = d_c, prove that .

See also: 

  Pythagoras Theorem
  Euclid's Elements Book II Proposition 13
  Median length, Apollonius' Theorem
  Problem 249