Pedal Triangles and the Simson Line
Given a triangle and its circumcircle with point (P) anywhere on the circumcircle.
By constructing perpendicular lines from (P) to each triangle side, we will form the pedal triangle of our original triangle.
The pedal triangle of triangle ABC is triangle PDF. The line through DF is the Simson Line of triangle ABC. This is the line, that when traced, will form a deltoid triangle.