If 
,
,
and 
are three conics having the property that there is a point 
, not on any of the conics, lying on a common chord of each
pair of the three conics (with the chords in question being distinct), then there
exists a conic 
that has a double contact with each of 
, 
, and 
(Evelyn et al. 1974, p. 18).
The converse of the theorem states that if three conics 
, 
, and 
all have double contact with another 
then each two of 
, 
, and 
have a "distinguished" pair of opposite common
chords, the three such pairs of common chords being the pairs of opposite sides of
a complete quadrangle (Evelyn et al. 1974,
p. 19).
The dual theorems are stated as follows. If three conics are such that, taken by pairs, they have couples of common tangents intersecting at three distinct points on a line (that is not itself a tangent to any of the conics), then (a) the conics have this property in four different ways, and (b) the conics all have double contact with a fourth. And, conversely, if three conics each have double contact with a fourth, then certain of their common tangents intersect by pairs at the vertices of a complete quadrilateral (Evelyn et al. 1974, p. 22).
A degenerate case of the theorem gives the result that the six similitude centers of three circles taken by pairs are the vertices of a complete quadrilateral (Evelyn et al. 1974, pp. 21-22).
