12. As shown in Figure 2, in $\triangle A B C$, $B C=a, A C=$ $b, A B=c$. If the medians $B E$ and $A D$ from $A C$ and $B C$ are perpendicular to each other at point $O$, then $c$ can be expressed as an algebraic expression in terms of $a$ and $b$
12. $c=\frac{1}{5} \sqrt{5\left(a^{2}+b^{2}\right)}$