A Pedal Triangle is formed from the following construction.
Let triangle ABC, be any triangle. If P is any point in the plane, then the triangle formed by constructing perpendiculars to the sides of ABC locate three points R, S, and T that are the intersections. Triangle RST is the Pedal Triangle for Pedal Point P.
First we will examine triangle ABC with point P in the plane, and its perpendiculars to the sides of ABC that creates the Pedal Triangle RST.
Now we will examine what happens to triangle RST, if P is on the side of triangle ABC:
Regardless of where it is placed on the side, you will notice that P becomes one of the vertices of triangle RST.
Now let us examine what happens with triangle RST, if P is placed at one of the vertices of triangle ABC:
Regardless of which vertex is used, you will notice that triangle RST collapses to one of the perpendicular bisectors of triangle ABC.