The Moses-Longuet-Higgins circle is the radical circle of the circles centered at the vertices 
, 
, and 
of a reference triangle
with respective radii 
, 
, and 
(P. Moses, pers. comm., Nov. 17, 2005).
Its center has triangle center function
 |
(1)
|
where 
,
,
and 
are Conway triangle notation, 
, 
, and 
. This is not a Kimberling
center.
It has radius
![R_(MLH)=sqrt(9R^2+4[1-(12(a+b+c)R^2)/(abc)]r^2),](/images/equations/Moses-Longuet-HigginsCircle/NumberedEquation2.svg) |
(2)
|
where 
is the circumradius and 
the inradius of the reference
triangle, and circle function
 |
(3)
|
which corresponds to Kimberling center 
.
