Villarceau Circles

How many circles can be drawn through an arbitrary point on a torus? Surprisingly, there are four. Two are obvious: One is parallel to the equatorial plane of the torus, and another is perpendicular to that.

The other two are produced by cutting the torus obliquely at a special angle. They’re named after French astronomer Yvon Villarceau, who first described them in 1848.