Circle Tangent on a sphere ?

 From:  Michael Gibson
5435.12 In reply to 5435.11 
You can also create a construction line along the sphere's surface normal to help in some kinds of constructions like this.

To do that start the construction line's first point on the sphere (object snap must be enabled), then when you drag out there will be a "normal" snap that you can use to place the other point along the sphere's surface normal. Straight snap must be enabled to get that kind of surface-normal snap.

- Michael