The following is a construction of the Pedal Triangle of triangle ABC, triangle RST is the Pedal Triangle:
For a GSP script click here.
The following will provide an illustration for when the point P is the Centroid (C), Incenter (IC), the Orthocenter (OR); and the Circumcenter (CC).
For a GSP script click here.
Point P is Centroid:
Point P is Incenter:
Point P is Orthocenter:
Point P is the Circumcenter:
