In this applet by Bob Allanson, the vertices A, B', C, A', B, C' (A) of the hexagon are constrained to lie on the circle (ellipse).

(a) Change the positions of these vertices and check if the crossing points L, M, N remain collinear.

(b) Check that the theorem remains true for the ellipse. Notice that you can change the scale in cases where the figure pushes the boundaries.