Geometric interpretation for median formula $m_c = \sqrt{\frac{2(a^2 + b^2)- c^2}{4}}$ for $a + b < c$? For a triangular with side lengths $a, b, c$, the length of the median of $c$ is $m_c = \sqrt{\frac{2(a^2 + b^2) - c^2}{4}}$.  
If $a + b < c$, the configuration is obviously not a triangle anymore. 
However, there are values for $a, b, c$ with $a + b < c$ (e.g. $a = 7, b = 2, c = 10$) where the root is still positive. Is there any geometric interpretation for that?

For the median, what we need is not just $m_c\ge0$. We actually need $\displaystyle m_c\ge\frac{|a-b|}{2}$.
When $a=7$ and $b=2$, $\displaystyle \frac{|a-b|}{2}=\frac{5}{2}$.
Now $\displaystyle \sqrt{\frac{2(a^2+b^2)-c^2}{4}}=\frac{\sqrt{6}}{2}<\frac{5}{2}$.
