Given a triangle 
,
the points 
, 
,
and 
lie on a line, where 
is the incenter and 
is the excenter corresponding
to 
. Furthermore, the circle
with 
as the diameter has 
as its center, where 
is the intersection of 
with the circumcircle
of 
, and passes through 
and 
.
This circle has radius
 |
It arises because 
forms an orthocentric
system.
