# 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 $b^{2}+c^{2}=2m^{2}+\frac{a^{2}}{2}$.

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

 $m^{2}+(a/2)^{2}=b^{2}.$
 Title Apollonius theorem 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