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.
