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Stewart's theorem (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 $AX$.

\includegraphics{stewart}
Then
\begin{displaymath}a(p^2+mn)=b^2m+c^2n.\end{displaymath}



"Stewart's theorem" is owned by drini. [ owner history (1) ]
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See Also: Apollonius theorem, cosines law, proof of Stewart's theorem, Stewart's theorem, proof of Apollonius theorem


Attachments:
proof of Stewart's theorem (Proof) by Mathprof
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Cross-references: length, point, triangle
There is 1 reference to this entry.

This is version 3 of Stewart's theorem, born on 2001-10-06, modified 2002-05-16.
Object id is 145, canonical name is StewartsTheorem.
Accessed 13220 times total.

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AMS MSC: 51-00 (Geometry :: General reference works )
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