The Dou circle is the circle cutting the sidelines of the reference triangle 
at 
, 
, 
,
, 
, and 
such that 
(i.e.,
all are right angles).
Its center is Kimberling center 
with center function
 |
(1)
|
and its radius is
 |
(2)
|
where 
is the circumradius
of the reference triangle and 
is an 18th-degree polynomial.
It has circle function
 |
(3)
|
which does not correspond to any Kimberling center.
No Kimberling centers lie on the Dou circle.
