The Simson Line

Let ΔABC be any triangle, and let P be any point in the plane. Construct lines through P which are perpendicular to each of the sides of ΔABC. Let D, E, and F be the points of intersection of these lines with the lines to which they are perpendicular. We call ΔDEF the pedal triangle for pedal point P. Click here for a GSP file demonstrating the construction of a pedal triangle.
In this GSP file, move the pedal point P around until the pedal triangle is degenerate. That is, find a location of P such that the pedal "triangle" just looks like a line segment. Such a segment is called the Simson line. Once you have found such a location for P, move one of the blue circles (in the upperleft corner of your screen) to that location to mark it.
Repeat this process several times, until you feel comfortable making a conjecture about where P must lie in order for the pedal triangle to be degenerate. What property do the locations of your blue circles seem to share? Do they lie on a single line? On a parabola? What? Make a conjecture before clicking here to continue.
