Let us call, for reasons discussed shortly (*), a simple

quadrilateral that has its opposite sides (or their extensions) going

through two of the vertices of a triangle ABC and its opposite

vertices on isogonal lines through the third vertex, a "perspective

parallelogram".

The four segments, joining the four vertices of a "perspective

parallelogram" with their four isogonal conjugates, are concurrent.

(*) If we perceive the three vertices of a triangle as the three

vanishing points of a three point perspective drawing (i.e., perceive

the three sides of the triangle as the three horizon lines of that

drawing), the statement of the message becomes self-evident. For a

brief discussion on the application of this view on similar problems,

see message 15247.