If two intersections of each pair of three conics , , and lie on a conic , then the lines joining the other two intersections of each
pair are concurrent (Evelyn et al. 1974, pp. 23
and 25).

The dual theorem states that if two common tangents of each pair of three conics touch a fourth conic, then the remaining common tangents of each pair intersect
in three collinear points (Evelyn et al. 1974,
pp. 24-25).