Min/Max Axis of a Circle or Cylinder

Min/Max Axis of a Circle or Cylinder

I am checking an aluminum ring about 9" dia. OD and 7.5" ID. It is from plate material and "relaxes" after removal from the machine. I think due to grain direction.

Is there a way to get the Diameter AND axis of the minimum and maximum diameters (distance across, not Max-inscribed or Min circumscribed)? How do I either create a line at these locations across the circle/cylinder or get an angle of the line across relative to the coordinate system?

Origin is at the center, and I thought of finding the closest point of the circle to the origin, but there is no guarantee the opposing point is equally close. And that won't work for the furthest (largest dia.) points.
Also there is no guarantee that the Min and Max diameter are 90 degrees to each other...

Thanks for any ideas you all may have.