By Amber Krug
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.
Below is an example of a Pedal Triangle:
If the pedal point is the orthocenter of ABC, then the one point of the pedal triangle is always shared with one point on ABC even if the orthocenter is outside the triangle.
If the pedal point is on one of the vertices of ABC, then one of three things can happen:
1. The pedal triangle is enlarged:
2. The pedal triangle becomes a line segment:
3. The pedal triangle becomes a point: