Figure 1: The conic Q(F)
 
Figure 1: The conic Q(F)

The defining sets that determine Q(F) are
S(F)={A, B, C, D, E},
S1(F)={A, B, C} and
S2(F)={D, E}.
In the dynamic figure, Q(F), as a whole, does not move as a function of F, but it does move as a function of each of the points of S(F).

The six lines AD, AE, BD, BE, CD and CE are shown as dotted lines.

The six points of intersection of these lines (other than those of S), form the hexagon {AE.BD, AE.CD, BE.CD, BE.AD, CE.AD, CE.BD}. The three pairs of opposite sides of the hexagon meet in the three points A, B and C. Since these points are collinear, the theorem of Pascal informs us that the six points of the hexagon lie on a conic. To put it another way, the conic through any five of the six points goes through the sixth.

The reader will notice that Q(F) appears to meet L1 in two points and appears to meet L2 not at all.


The Cabri Geometry II source code is available for all figures used in this paper, as well as demonstration versions of Cabri Geometry II for Windows and Macintosh operating systems.
© 1997, 1999, Leroy J. Dickey