This theorem reminds me of the Wallace-Simpson line in a triangle. The Wallace-Simpson line is constructed by dropping perpendiculars to the sides (extended) of a triangle from a point on the circumcircle. The feet of these perpendiculars lie on a line. This line is the Wallace-Simpson line.
In the complete quadrilateral, from the Focus Point, we drop perpendiculars to the sides of the quadrilateral. The feet of these perpendiculars are also collinear. This is known as the Pedal Line. The proof of this follows directly from the Wallace-Simpson line.