The eight circles theorem is a theorem about a closed chain of six circles whose consecutive intersections lie on two additional circles. It asserts that the lines joining opposite pairs of centers in the chain are concurrent, with parallel lines allowed as concurrence at a point at infinity.
More precisely, let 
, ..., 
be six distinct points on a circle 
, and let 
lie on another circle 
. For 
, ..., 5, let the circle
through 
, 
, and 
meet 
again at 
. Then 
, 
, 
, and 
are concyclic. Let 
be the center of the circle
through 
, 
, 
, and 
, taking subscripts modulo
6. Assume that all these circles are well-defined ordinary
circles, that the second intersections
are distinct, and that each pair 
, 
consists of distinct points.
Then 
, 
, and 
are concurrent or parallel
(Dao and Perng 2019, p. 49).
