Creating perfect circular dimple (cut) on a circular surface (ring)

I have a ring and on the surface of that ring I am trying to create a perfect cicle dimple cut.  The problem is that since the surface I'm trying to cut into is circular the round dimple turns into an oval.  Is there any way to make this feature so that looking down on the ring, this dimple looks like a perfect circle? Here is a picture of the ovular dimple on the ring.

Hopefully I've explained myself. 

Thanks