Figure 3: Six Conics
 
Figure 3: Six Conics

Six conics Q(A), Q(B), Q(C), Q(D), Q(E) and Q(F) are shown.

The three conics Q(A), Q(B) and Q(C) all meet at two points U1 and U2 on the line L2. Both of these points are labeled U in the figure.

As discussed in Figure 2, the three conics Q(D) Q(E) and Q(F) meet at two points T1 and T2 on the line L1. Both of these points are labeled by T in the figure.

All six conics meet at two more points V1 and V2 which are both labeled by V in the figure. Neither V1 nor V2 lies on L1 or L2.

Any line through one of the T points and one of the U points also passes through one of the V points.

The two points T1 and T2 on the line L2 are invariant as functions of D or E or F.

Likewise, the two points U1 and U2 on the line L1 are invariant as functions of A or B or C.

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