If three conics pass through two given points 
and 
, then the lines joining the other two intersections of each
pair of conics 
are concurrent at a point 
(Evelyn 1974, p. 15). The converse states that if two
conics 
and 
meet at four points 
,
,
,
and 
,
and if 
and 
are chords of 
and 
,
respectively, which meet on 
, then the six points lie on a conic. The dual of the
theorem states that if three conics share two common tangents, then their remaining
pairs of common tangents intersect at three collinear
points.
If the points 
and 
are taken as the points at infinity, then the
theorem reduces to the theorem that radical lines
of three circles are concurrent
in a point known as the radical center (Evelyn
1974, p. 15).
If two of the points 
and 
are taken as the points
at infinity, then the theorem becomes that if two circles 
and 
pass through two points 
and 
on a conic 
, then the lines determined by the pair of intersections of
each circle with the conic are parallel (Evelyn 1974, p. 15).
