Pascal's hexagon theorem
A few months ago I found an inspiring illustration of Pascal's hexagon theorem at Bruce Shawyer's web page in geometry. Because of its generality it is not easy to create a failsafe dynamic presentation of the theorem in general. In this applet I implemented only a special case, namely the circle.
The statement, that is, the collinearity of some intersection points, still holds for all conic sections (including ellipse, parabola, hyperbola and two lines). Here is Bruce's illustration for an ellipse:
