How can I determine/calculate a circumcenter with 3 points I wanted to calculate the circumcenter of an object (for example of an cylinder).

For this purpose I use Z-mode to see the grid of an object and mark three points that are on the same circle. After this I calculate the circumcenter on paper and set my 3D cursor to those values.

Is there an addon/widget/plugin/script that I can add to Blender to archive the same without the hassle of manually calculating or can Blender do that by itself?

The main goal I have is to get the midpoint of a circle object in Blender. If the calculation with 3 points is unneeded and over complicating things tell me so please.

Furthermore sadly I do not find calculators online who support 3D vectors for this calculation. So If you can link me a calculator for tempory usage would be great too.
I have written such a tool, it creates a grease-pencil representation of the reconstructed circle if you can select 3 vertices of an incomplete circle. It also allows you to change the number of vertices of the new representation.

You can easily convert from grease pencil to mesh

6 mb example image