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 
is the point opposite 
on the circumcircle. The
circle with diameter 
also passes through 
and 
and has radius
 |
It arises because the points 
, 
, 
, and 
form an orthocentric
system.
