The Simson Line
In the figure below, the Simson line (in red) is the line that joins the “feet” of the perpendiculars of the extended sides of triangle ABC from any point (noted as P) on the circumcircle of the triangle ABC. The Simson line can also be defined as when all three of the vertices (LMN in the figure below) of the pedal triangle are collinear. This is due to the fact that the pedal point (or point P) is found on the circumcircle of the triangle ABC. The pedal triangle, in general, is obtained by dropping perpendicular lines from a point (point P) to the sides of the triangle ABC.