Try moving the points A, B, C, D, E and F by dragging the circles on the screen. As you move the points A-E, an ellipse
is drawn which passes through those points. As you move the point F, note the intersections between the line
AF and the line DC, between the line DE and the line AB, and between the line BC and the line
EF. (Notice that these are lines, not line segments - the part of the line "outside"
the line segment is displayed dotted, if necessary.) If F is not on the ellipse, then these three points of intersection
will form a nondegenerate triangle. If F is on the ellipse, all three of those intersections will be collinear. (The
orange triangle will degenerate to a line segment.) Try moving F along the ellipse and see what happens.