Two questions:

Exactly how is the given circle identified without identifying a center point or a point whose distance from the center point represents the circle radius? This makes little sense either theoretically or mechanically. At least, my compass can not do it. Maybe there needs to be a new postulate to Euclid's elements that every circle has a center point.

Does not the "transformation" of the circle (in three dimensions) represent a "redrawing" of the circle; and hence, breaks the rule of only using a straightedge? If not, then it implies a mechanical transformation, which invalidates the anti-proof.