Stewart's Theorem
Let a Cevian 
be drawn on a Triangle 
, and denote the lengths 
and 
, with 
. Then
This theorem is sometimes also called Apollonius' Theorem.
References
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.
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