Countless Simson line configurations

Abstract

The Simson line property is normally associated with points on the circumcircle of a triangle. It is embodied by the following theorem.Given any triangle ABC and a point P in the plane of the triangle, if perpendiculars from P on to the sides BC, CA, AB meet those sides at L, M, N respectively then L, M, N are collinear if and only if P lies on the circumcircle of triangle ABC. The line LMN is then known as the Simson line of P.