Pedal Triangles
by
Bradley Johnson
The pedal triangle of any given triangle is constructed as the triangle whose vertices are given by the intersection of a line through a chosen point (called the pedal point), perpendicular to each of the sides of the triangle. Here is a script tool that will construct a triangle along with its pedal triangle.
If we let the pedal point be outside of the original triangle we have something that looks like this:
Moving the pedal point to various other locations results in some interesting properties. If we let the pedal point be one of the vertices of the triangle the pedal triangle collapses and becomes a line:
When the pedal point coincides with the point of the pedal triangle that lies on one side of the original triangle we obtain a pedal triangle in which one side lies along the side of the original triangle:
