The difficult part of the question is that the circle is really a 3D
object
ie it can be rotate about the x or y axis.
Do you mean rotate into the "z" axis? X and Y are still just 2-D
spaces.
'rotating around the x-axis' is a perfectly reasonable statement for
a 3D object: rotate something in the x-y plane by 90 degrees about
the x-axis and it will end up in the x-z plane. Rotating around the
z-axis would keep it in the same plane. You can't rotate a 2-d
object about an axis at all, only a point.
Well, then, if you rotate a circle around the global x or y axis by
90 degrees (picture a coin standing on edge), the radius of the
largest circle that would fit in a rectangular bounding box would be
1/2 the diagonal of that rectangle, or ((x^2 + y^2)^0.5)/2.
...because you can then rotate the circle around the global z axis
until its local x-y plane is parallel to the diagonal of the
rectangle.
OP, is that what you were looking for?
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