The pedal circle with respect to a pedal point 
of a triangle 
is the circumcircle
of the pedal triangle 
with respect to 
. Amazingly, the vertices of the pedal
triangle 
of the isogonal conjugate point 
of 
also lie on the same circle (Honsberger 1995). If the pedal
point is taken as the incenter, the pedal circle
is given by the incircle.
The radius of the pedal circle of a point 
is
 |
(Johnson 1929, p. 141).
When 
is on a side of the triangle,
the line between the two perpendiculars is called the pedal
line. Given four points, no three of which are collinear,
then the four pedal circles of each point for the triangle
formed by the other three have a common point through which the nine-point
circles of the four triangles pass.
