Michael Thomason's write-up for assignment nine, question seven.

Let triangle ABC be any triangle. Then if P is any point in the plane, then the triangle formed by constructing perpendiculars to the sides of ABC (extended if necessary) locate three points R, S, and T that are the intersections. Triangle RST is the Pedal Triangle for Pedal Point P.

Here are a few pictures of the pedal triangle RST for a fixed triangle ABC with P in different locations:

Click here to open a GSP file with the above triangle and pedal triangle. See what happens when you move P to various locations. There is also a script tool called “Pedal Triangle” that will construct the pedal triangle for a given triangle and pedal point.

What if P is on a side of the original triangle? Here are a few pictures:

The angle RPS remains the same regardless of P’s position along . In addition, RPS + ABC always equals 180˚. Click here to see an animation that shows this. Note that RPS + ABC always equals 180˚ even if you change the location of points A, B, and/or C.