Only 3D software. Illustrator doesn't have a tool like this, + for Designer. :-)
But if you use, say, the Tube Object in Cinema 4D, you can use "Slice" to make the same thing.
And if you would ever convert that into polygons (in your case, to curves), it would not all of a sudden close the sliced curve in bad topology?
Meaning, if you use the Pie tool and make it turn into just an outline of a 3rd circle, it would convert into an open curve, not a closed with half of it hidden in the exact same location?