Geometry, Theorems and Problems

 Problem 255. Triangle, Centroid, Vertices, Interior/Exterior 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. If
BC =a, AC = b, AB = c, AE = ea, BE = eb, CE = ec, and EG = m, prove that Problem 255: Formula to proof.
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Elearning: triangle, centroid and distances

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

  Problem 253
  Problem 254

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