# Bitangent

In mathematics, a bitangent to a curve C is a line L that touches C in two distinct points P and Q and that has the same direction to C at these points. That is, L is a tangent line at P and at Q.

Read more about Bitangent:  Bitangents of Algebraic Curves, Bitangents of Polygons, Related Concepts

### Other articles related to "bitangent, bitangents":

Bitangent - Related Concepts
... A bitangent differs from a secant line in that a secant line may cross the curve at the two points it intersects it ... One can also consider bitangents that are not lines for instance, the symmetry set of a curve is the locus of centers of circles that are tangent to the curve in two points ... Bitangents to pairs of circles figure prominently in Jakob Steiner's 1826 construction of the malfatti circles and in the belt problem of calculating the length of a belt connecting two pulleys ...
Malfatti Circles - Steiner's Construction
... Each pair of two of these three inscribed circles has two bitangents, lines that touch both of the dashed circles and pass between them one bitangent is the angle bisector, and the second ... Label the three sides of the given triangle as a, b, and c, and label the three bitangents that are not angle bisectors as x, y, and z, where x is the bitangent to the two circles that do not touch side a, y is the ... The three bitangents x, y, and z cross the triangle sides at the point of tangency with the third inscribed circle, and may also be found as the reflections of the angle bisectors across the lines ...
Tangent Lines To Circles - Tangent Lines To Two Circles - Degenerate Cases
... Two distinct circles may between zero and four bitangent lines, depending on configuration these can be classified in terms of the distance between the centers and the radii ... If counted with multiplicity (counting a common tangent twice) there are zero, two, or four bitangent lines ... Bitangent lines can also be generalized to circles with negative or zero radius ...
Villarceau Circles - Existence and Equations
... and choosing the plus sign produces the equation of a plane bitangent to the torus By symmetry, rotations of this plane around the z axis give all the bitangent planes through the center ... Furthermore, it is included in every bitangent plane ... conic, and shows that intersection with a bitangent plane must produce two conics of the same type as the generator when the intersection curve is real ...