Pushing the Pedal to the Limit!
P is the pedal point of triangle ABC.†
RST is the pedal triangle for pedal point P.
Another interesting observation regarding the pedal point is that once the three perpendiculars have passed through any two vertices of the triangle ABC, the pedal triangle disappears.†
Pedal points are not traditionally taught in secondary geometry, even at the honors or gifted level, but some of the properties are very applicable particularly to honors and gifted students because some of these ideas and concepts are good introductions to higher level thinking that will be required in calculus.†