Snap to surface

 From:  Michael Gibson
3578.3 In reply to 3578.2 
Hi Joe, welcome to MoI! It sounds like you have got your problem figured out already?

Yeah by its nature drawing a circle on a sphere will make the circle kind of skim the sphere and not be sunken down into it, but like you found enabling the "both sides" option for extrude will solve that by punching the shape out in both directions and getting it to punch into the sphere.

- Michael