Given any triangle ABC. Then if P is any point in the plane, then the triangle formed by constructing perpendiculars to the sides of ABC (extended if necessary) locate three points R,S, and T that are the intersections. Triangle RST is the Pedal Triangle for Pedal Point P. Click here for GSP script of Pedal Triangle.

What if pedal point P is on a side of the triangle ?

Then P and vertex of the side of pedal triangle are same as following.

If P is one on the vertexes then P and two vertexes of pedal triangle are same, and pedal triangle is segment. When P is outside of triangle ABC, if P and one of the vertexes of pedal triangle is same, P is on the extend line of the side.

What if pedal point P is the centroind of triangle ABC ? Click here for GSP script of centroid.

What if pedal point P is the incenter of triangle ABC ? Click here for GSP script of incenter. Click here.

What if pedal point P is the Orthocenter of triangle ABC ? Even if outside ABC? Click here for GSP script of Orthocenter.

What if pedal point P is the Circumcenter of triangle ABC ? Even if outside ABC? Click here for GSP script of Circumcenter.

What if pedal point P is the center of nine point circle of triangle ABC ? Click here for GSP script of the center of nine point of circle.

Find all conditions in which the three vertices of the Pedal triangle are colinear (that is, it is a degenerate triangle). This line segment is called the Simson Line.