[MrQuincle]

It is possible to pick three distinct points, which uniquely identify a circle, and map this to a Hough space.

It is called the randomized Hough transform.

https://en.wikipedia.org/wiki/Randomized_Hough_transform

Circular arcs is stretching it. :-) Do you need to find the endpoints of the arc? That would be two more dimensions to search over. If that's the case I would just use a maximum likelihood approach. You have to be careful in that case, if you have a circle the distance of points on the inside of the circle and points on the outside of the circle meshes up any naive fitting method.