Does there exist a circle, on the surface of a torus, that is not coplanar with the axis of revolution? I have got two closely related questions regarding Tori. 
1.Does there exist a circle, on the surface of a torus, that is not co planar with the torus' axis of revolution?
2.Can the centre of a circle that is lying on the surface of a torus be the centre of a different circle also lying on the surface of the torus?
How does one proceed with proving (or disproving) them?

Provided that your torus bows to 2r=R, then a pair of those Villarceau circles can be chosen to conform with your nr. 2.
--- rk
