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Given an arbitrary point on a Torus, four Circles can be drawn through it. The first is in the plane of the torus and the second is Perpendicular to it. The third and fourth Circles are called Villarceau circles.
See also Torus
References
Melzak, Z. A. Invitation to Geometry. New York: Wiley, pp. 63-72, 1983.
Villarceau, M. ``Théorème sur le tore.'' Nouv. Ann. Math. 7, 345-347, 1848.