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
Canonical name	LengthsOfTriangleMedians
Date of creation	2013-03-22 18:26:47
Last modified on	2013-03-22 18:26:47
Owner	pahio (2872)
Last modified by	pahio (2872)
Numerical id	5
Author	pahio (2872)
Entry type	Corollary
Classification	msc 51M04
Synonym	lengths of medians
Related topic	ProofOfApolloniusTheorem
Related topic	CommonPointOfTriangleMedians
Related topic	LengthsOfAngleBisectors