Stewart’s theorem

Let be given a triangle $\mathrm{△}ABC$ 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