Pascal's Theorem

Two sets of points - A, B, C and A',B',C' are drawn on an ellipse. [you can adjust the size and shape of the ellipse by dragging the purple dots] The following sets of lines are drawn - AB' and BA' AC' and CA' BC' and CB' Each of these sets of lines intersect at a point. Drag the points to persuade yourself that the three intersection points always lie on a straight line. Can you explain why this is so? What questions could/would you put to your students based on this applet?