KöMaL 2018 B4923

The interior angle bisector drawn from vertex $A$ of triangle $ABC$ intersects side $BC$ at $E$, and the interior angle bisector drawn from vertex $B$ intersects side $AC$ at $F$. Let $O$ denote the centre of the inscribed circle of the triangle. What may be the size of the angle at $C$ if the sum of the areas of $\triangle OFA$ and $\triangle OBE$ equals the area of $\triangle AOB$?