Alternatively, the center may be omitted with sufficient additional information. This is not a weakening of the Poncelet-Steiner theorem, merely an alternative framework. Nor is it a contradiction of Steiner's Theorem which hypothesizes only a single circle. The inclusion of this sufficient alternative information disambiguates the mappings under the projective transformations, thus allowing various Steiner constructions to recover the circle center. Some alternatives include two concentric or two intersecting circles, or three circles, or other variations wherein the provided circle(s) are devoid of their centers, but some other unique but sufficient criterion is met. In any of these cases, the center of a circle can be constructed, thereby reducing the problem to the Poncelet-Steiner theorem hypothesis (with the added convenience of having additional circles in the plane).
