KöMaL 2010 A522

The vertices and side arcs of the spherical hexagon ABCDEF are located on a hemisphere. The arc $AB$ is perpendicular to the arc $BC$, the arc $AF$ is perpendicular to the arc $EF$, moreover $AB$=$AF$, $BC$=$CD$ and $DE$=$EF$. Prove that the great arcs $AD$ and $CE$ are perpendicular.