Pedal
Triangles and the Simson Line

Erin
Mueller

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.