By definition: Let O and A be 2 points in E^2 space. A circle of radius OA would be the unioun, that is, locus of points of all points X that satisfy d(O,X) = d(O,A) where d is the distance of the points. Similar for E^3 that is: sphere. It gets more interesting when we add a n>3 in E^n.
So the construction of a circle can be achieved perfectly using an isometric transformation that rotates point A around point O an infinite amount by an infinetely small angle. Then, pie and cake may be had by all.