When P is any vertex of triangle ABC:
The vertices of the pedal triangle are colinear forming the altitude from
that point to the opposite side. This degenerate triangle is called the
Simpson Line.
When P is the centroid (G) of triangle ABC:
The pedal triangle is the medial triangle.
When P is the orthocenter (H) of triangle ABC:
The pedal triangle is the orthic triangle.
When P is the incenter (I) of triangle ABC:
The vertices of the pedal triangle are the points of intersection of the
incircle and the sides of triangle ABC.
When P is on the circumcircle.
The pedal triangle is also the simpson line. Click Here
to view the pedal triangle for any point on the circumcircle.