# lengths of triangle medians

By the Apollonius theorem, in any triangle, the $m_{a}$, $m_{b}$, $m_{c}$ of the medians (http://planetmath.org/Median) of opposing the the sides $a$, $b$, $c$, respectively, are

 $m_{a}=\frac{1}{2}\sqrt{2b^{2}+2c^{2}-a^{2}},$
 $m_{b}=\frac{1}{2}\sqrt{2c^{2}+2a^{2}-b^{2}},$
 $m_{c}=\frac{1}{2}\sqrt{2a^{2}+2b^{2}-c^{2}}.$
Title lengths of triangle medians LengthsOfTriangleMedians 2013-03-22 18:26:47 2013-03-22 18:26:47 pahio (2872) pahio (2872) 5 pahio (2872) Corollary msc 51M04 lengths of medians ProofOfApolloniusTheorem CommonPointOfTriangleMedians LengthsOfAngleBisectors