For a triangle ABC and a point P, there is a triangle that can be constructed by constructing perpendicular lines through P and each side of triangle ABC. The intersections of the perpendicular lines form the triangle RST.
Here is an example of the pedal triangle:
More specifically, this is the pedal triangle created when p is a point in the plane but outside of the circle.
Click Here to manipulate the Pedal Triangle in GSP.
From the images to the left it can be seen that as the point P is placed on each vertex, the triangle seems to dissolve and become a straight line going through the vertex and a point on the opposite side. 

We can see that when the point P is located on a segment of triangle ABC, it follows that a triangle will be created which is located within the triangle ABC.  