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editThis is new to me, and I cannot find any reference of this.
The Poncelet points of two circles, C1 and C2, that have no point in common, are: the two point circles (radius 0) belonging to the pencil of circles determined by C1 and C2.
See: Pierre Samuel, Projective Geometry, Springer 1988. Ldboer (talk) 13:20, 2 July 2010 (UTC)