Bitangent

In general, an algebraic curve will have infinitely many secant lines, but only finitely many bitangents.

Bézout's theorem implies that an algebraic plane curve with a bitangent must have degree at least 4.

The case of the 28 bitangents of a quartic was a celebrated piece of geometry of the nineteenth century, a relationship being shown to the 27 lines on the cubic surface.

This bitangent calculation is a key subroutine in data structures for maintaining convex hulls dynamically (Overmars & van Leeuwen 1981).

Bitangents may be used to speed up the visibility graph approach to solving the Euclidean shortest path problem: the shortest path among a collection of polygonal obstacles may only enter or leave the boundary of an obstacle along one of its bitangents, so the shortest path can be found by applying Dijkstra's algorithm to a subgraph of the visibility graph formed by the visibility edges that lie on bitangent lines (Rohnert 1986).