If a cyclic quadrilateral 
is inscribed in a circle 
of a coaxal system such
that one pair 
of connectors touches another circle 
of the system at 
, then each pair of opposite connectors will touch a circle
of the system (
at 
on 
,
at 
on 
,
at 
on 
,
at 
on 
,
and 
at 
on 
),
and the six points of contact 
, 
, 
, 
, 
, and 
will be collinear.
The general theorem states that if 
, 
, ..., 
are any number of points taken in order on a circle
of a given coaxal system so that 
, 
, ..., 
touch respectively 
fixed circles 
, 
, ..., 
of the system, then 
must touch a fixed circle 
of the system. Further, if 
, 
, ..., 
touch respectively any 
of the circles 
, 
, ..., 
, then 
must touch the remaining circle.
