Median Formula

Theorem
the Length of Medians is equal to

$$m_a^2=\dfrac{c^2}{2}+\dfrac{b^2}{2}-\dfrac{a^2}{4}$$

$$m_b^2=\dfrac{c^2}{2}+\dfrac{a^2}{2}-\dfrac{b^2}{4}$$

$$m_c^2=\dfrac{a^2}{2}+\dfrac{b^2}{2}-\dfrac{c^2}{4}$$

where $$m_a$$,$$m_b$$ and $$m_c$$ are the medians from A,B and C respectively

Proof
We use Stewart's Theorem then $$AP=PB=\dfrac{c}{2}$$ and $$CP = m_c$$

now we have

$$ $$ $$

A similar argument can be used to show that the statement holds for the others medians