# Stewart’s theorem

Let be given a triangle $\triangle ABC$ with $AB=c$, $BC=a$, $CA=b$, and a point $X$ on $BC$ such that $BX=m$ and $XC=n$. Denote with $p$ the length of $AX$.

Then

 $a(p^{2}+mn)=b^{2}m+c^{2}n.$
 Title Stewart’s theorem Canonical name StewartsTheorem Date of creation 2013-03-22 11:44:07 Last modified on 2013-03-22 11:44:07 Owner drini (3) Last modified by drini (3) Numerical id 11 Author drini (3) Entry type Theorem Classification msc 51-00 Classification msc 65-00 Classification msc 81-00 Related topic ApolloniusTheorem Related topic CosinesLaw Related topic ProofOfStewartsTheorem Related topic StewartsTheorem Related topic ProofOfApolloniusTheorem2