The figure shows an equilateral triangle ABC. If a point D is on the incircle, E, F, and G are the points of tangency,
DE = d, DG = e, DF = f, DA = m, DB = n, and DC = q, prove that . View or post a solution.

See also: 

  Median length, Apollonius' Theorem
  Euclid's Elements Book II Proposition 13
  Problem 259
  Problem 258
..Problem 257
  Problem 256
  Equilateral Triangle