If perpendiculars ,
, and are dropped on any line from the vertices of a triangle , then the perpendiculars to the
opposite sides from their perpendicular feet , , and are concurrent at a point
called the orthopole. The orthopole
of a line lies on the Simson line which is perpendicular
to it (Honsberger 1995, p. 130). If a line crosses the circumcircle
of a triangle, the Simson lines of the points of intersection
meet at the orthopole of the line. Also, the orthopole of a line through the circumcenter of a triangle lies on that triangle's nine-point
circle (Honsberger 1995, p. 127).

If the line
is displaced parallel to itself, the orthopole moves
along a line perpendicular to a distance equal to the displacement. If is the Simson line of a point
, then is called the Simson line pole
of (Honsberger 1995, p. 128).

The orthopole of a line
is equivalent to the orthojoin of Kimberling center .

The following table summarized the orthopoles for some named central lines.