Maybe a NODE could be created, which performs the Rotation of unit chord, 3point circle, and OrientLineLine ???
Then something to check the ERROR of the Top Center intersection point versus the top center of the circle.
Make successive corrections to the angle.

- Brian

ps
I used MoI Dimension Angle to measure angles.
The upper unit chord angle is 114.844058, for the candidate circle.
Maybe the average with the other 114+ angle could be useful?

The perpendicular bisectors are not quite intersecting at the successive circle centers.