While it is easy to get the incirlce/excircle of a triangular profile (using the 3-tangent or 3-point circle), it would be also very convenient if there would be an easy option to get a vertex at the centroid of any closed profile and/or at the center point of a circumcircle of any closed profile.
This could either be a "automatic snap point" such as line-midpoints are, or an option/constraint for a manually added vertex.
The defining (closed) profile would be the same one, one selects when double-clicking an edge (to disambiguate from sub-profiles which are created by adding lines etc.)