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Stewart's Theorem

\begin{figure}\begin{center}\BoxedEPSF{StewartsTheorem.epsf scaled 800}\end{center}\end{figure}

Let a Cevian $A_1P$ be drawn on a Triangle $\Delta A_1A_2A_3$, and denote the lengths $m=\overline{A_2P}$ and $n=\overline{PA_3}$, with $a_1=m+n$. Then


This theorem is sometimes also called Apollonius' Theorem.


Altshiller-Court, N. ``Stewart's Theorem.'' §6B in College Geometry: A Second Course in Plane Geometry for Colleges and Normal Schools, 2nd ed., rev. enl. New York: Barnes and Noble, pp. 152-153, 1952.

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., p. 6, 1967.

© 1996-9 Eric W. Weisstein