KöMaL 2011 B4408

In a triangle ABC , the lengths of sides $AC$ and $BC$ are fixed, and the angle at vertex $C$ is variable. The midpoint of side $AC$ is $M$, the midpoint of side $BC$is $N$, and the centre of the square drawn over the side $AB$ on the outside is $O$. For what value of $ACB\sphericalangle$ will the sum of the distances $OM$ and $ON$be a maximum?