Now introduce a lip - and a third curve. Three curves to play with. Should they all be quadrants of circles, quadrants of ovals, or a mix of the two?
Here are some examples of Three Arcs pieces - circle quadrants, oval quadrants and a mix. These examples are just to get you thinking about playing with and blending arcs and locating the tangent points so don't get locked in on any specifics.
What if we flip the curve of the lip - inward?