Apollonius theorem

Let a,b,c the sides of a triangle and m the length of the median to the side with length a. Then b2+c2=2m2+a22.

If b=c (the triangle is isosceles), then the theorem reduces to the Pythagorean theoremMathworldPlanetmathPlanetmath,

Title Apollonius theoremMathworldPlanetmath
Canonical name ApolloniusTheorem
Date of creation 2013-03-22 11:44:10
Last modified on 2013-03-22 11:44:10
Owner yark (2760)
Last modified by yark (2760)
Numerical id 14
Author yark (2760)
Entry type Theorem
Classification msc 51-00
Classification msc 18-00
Classification msc 81-00
Related topic Triangle
Related topic Median
Related topic StewartsTheorem
Related topic ProofOfStewartsTheorem
Related topic ProofOfApolloniusTheorem2
Related topic ParallelogramLaw
Related topic ProofOfParallelogramLaw