I think that the original question was how to find the centre of a scribed circle. With a pair of dividers put a leg on the circle then guess the diameter and scribe an arc roughly around the centre. scribe another arc from a third around then another arc from 2/3rds around. you should then get a very small ” triangle” enclosing the true centre. ( I should have called the triangle a cocked hat)
This is an approximate method, you don’t have to be very precise but the “triangle” is very quick to draw and makes the guess very much better.
An accurate method. Chuck a point in the mill then place the point roughly over the middle. wind out the X axis past the circle then wind back to be over the circle, note the dial reading then carry on to the other side of the circle to get a second reading. Halve the readings to get the centre of the chord that you have just gone across and wind the x axis to the middle. you are now on a diameter of the circle.
Now do the same on the Y axis to find the middle of the tangent to the chord which is the centre of the circle. You do need always to work in the same direction to avoid backlash. drop the z axis to make a tiny centre mark.
Another version… draw a line across the circle intersecting the circle each side- roughly on the diameter. Set the dividers to the two crossing points, draw an arc from each point to intersect in two points each side of the line. join the crossing points with a straight line- this line is now on the diameter. From the two points where the diameter crosses the circle draw two arcs to intersect then join to find the true centre.
Billy.