Griffiths' theorem states that when a point 
moves along a fixed line 
through the circumcenter
of a given triangle 
and remains off its circumcircle,
the pedal circle of 
with respect to 
passes through a fixed point
on the nine-point circle of 
. This point is the orthopole
of 
with respect to 
and depends on 
(Goormaghtigh 1926, p. 92). When 
lies on the circumcircle,
its pedal circle degenerates to a Simson
line, which also passes through the orthopole.
This line-dependent fixed point is also called a Griffiths point and is distinct from the Griffiths points that are triangle centers. Given four distinct points on a circle and a fixed line through the center of the circle, the orthopoles of the line with respect to the four triangles formed by choosing three of the points are collinear (Tabov 1995).
