that's more of a workaround but here is what you could try:
#1 Snap->Snap Intersection
#2 Modify->Divide => select the first arc and then press on the first intersection (of both arcs)
=> select the first arc and then press on the second intersection
=> select the second arc and then press on the first intersection
=> select the second arc and then press on the second intersection
Now select both created arc segments and try to use hatching on them.