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.

   A circle is a 2d object, do you mean a cylinder?

The radius would always remain the same, 1/2 the shortest side of the box, or, if the box is aquare, call it 1/2 the width, it is the pespective that would change.

ryanm
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