This topic is more of pure mathematics, but all calculations are done on Mathematica so I put it here.
One day the question arose: how to determine centroid of annulus to be in the specified place?

Of course, it can't be usual centroid as a mass center. We can use symmetry, radius and concentric circle for geometric definition.
But this is not suitable for more general cases:

This led me to investigate the question of the types of centroids of shapes, which produced interesting results.
In particular, a simple definition for the specified center was found:

The point that minimizes the difference between maximum and minimum distance (inside figure) to the boundary

The analysis was conducted on Mathematica 13 using DiscretizeRegion and MeshConnectivityGraph
I have not yet published contributions for Wolfram Community and would like to ask:

• Perhaps someone has met the above definition (in more detail on stackexchange)
• In any case, would it be useful to publish in 3-4 groups a small study of this subject using cool Mathematica features?