To draw a conic section using Brianchon's theorem, we take one intersection from each pair of tangents as the vertices of a pentagram. We would like to avoid polygons that look crazy and are hard to draw from.
When we work by hand, we draw the tangents, arrange the intersections in a natural way, and [i]then[/i] number them.
Here is a scheme for mitigating the craziness at the computer. This method produces well-behaved pentagrams, regardless of the initial indexing of the tangents.
