The three conics theorem states that 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).
