proof of Apollonius theorem

Let m be a median of the triangle, as shown in the figure.

By Stewart’s theorem we have


and thus


Multiplying both sides by 2 gives



Title proof of Apollonius theoremPlanetmathPlanetmath
Canonical name ProofOfApolloniusTheorem1
Date of creation 2013-03-22 12:41:20
Last modified on 2013-03-22 12:41:20
Owner drini (3)
Last modified by drini (3)
Numerical id 5
Author drini (3)
Entry type Proof
Classification msc 51-00
Related topic Median
Related topic Cevian
Related topic ApolloniusTheorem
Related topic StewartsTheorem
Related topic ProofOfStewartsTheorem
Related topic ProofOfApolloniusTheorem