proof of Apollonius theorem

Let b=CA¯, a=BC¯, c=AB¯, and m=AM¯. Let CMA=θ, so that BMA=π-θ.

By the law of cosines, b2=m2+a24-amcosθ and c2=m2+a24-amcos(π-θ)=m2+a24+amcosθ, and adding gives



Title proof of Apollonius theoremPlanetmathPlanetmath
Canonical name ProofOfApolloniusTheorem
Date of creation 2013-03-22 12:41:16
Last modified on 2013-03-22 12:41:16
Owner quincynoodles (312)
Last modified by quincynoodles (312)
Numerical id 4
Author quincynoodles (312)
Entry type Proof
Classification msc 51-00
Related topic ProofOfApolloniusTheorem2
Related topic LengthsOfTriangleMedians