Geometry, Theorems and Problems

 Problem 254. Triangle, Centroid, Vertices, any Point, Distances, Squares

The figure shows a triangle ABC. G is the centroid G (point of concurrency of the triangle's medians) and E is any point (interior/exterior). If AG = da, BG = db, CG = dc, AE = ea, BE = eb, CE = ec, and EG = m, prove that Triangle centroid formula. View or post a solution.
 

Triangle, Centroid, Interior Point
 

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

  Problem 253
 

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