In mathematics, a bitangent to a curve C is a line L that touches it in two distinct points P and Q . That is, L is an tangent line at P and at Q .
Bézout s theorem implies that a plane curve with a bitangent must have degree at least 4. The case of the 28 bitangents to a general plane quartic curve was a celebrated piece of geometry of the nineteenth century, a relationship being shown to the 27 lines on the cubic surface. Such bitangents are in general defined over the complex numbers, and are not real (see Salmon s Higher Plane Curves ).