While the pedal point, Cevian point, and even pedal-Cevian point are
commonly used concepts in triangle geometry, there seems to be no established term
to describe the partitioning of an original triangle 
into three subtriangles 
, 
, and 
by the selection of a point 
. In this work, this process will be called triangulation (by
analogy with more general use of that term), and the point 
used to construct such a triangulation will be called a triangulation
point.
There is a remarkable series of theorems involving the triangles produced from an original triangle by triangulation. Let 
be a triangle center that
is also a triangulation point, and call three triangles produced from an initial
triangle 
by this point the triangulation triangles of 
. Then a remarkable number of triangle centers obey the following
theorem: If 
is a triangle center of a triangle 
and 
, 
, and 
are the corresponding centers of the triangulation triangles
of 
with respect to 
,
then the lines 
,
,
and 
concur. A number of special cases are summarized in the table below (Hatzipolakis
1999).
is the isogonal conjugate of the complement
of the symmedian point 
.
