Secant line

In geometry, a secant is a line that intersects a curve at a minimum of two distinct points.

A chord is the line segment that joins two distinct points of a circle.

In some situations phrasing results in terms of secant lines instead of chords can help to unify statements.

However, Robert Simson following Christopher Clavius demonstrated this result, sometimes called the intersecting secants theorem, in their commentaries on Euclid.

This definition leaves open the possibility that the line may have other points of intersection with the curve.

Secants may be used to approximate the tangent line to a curve, at some point P, if it exists.

The concept of a secant line can be applied in a more general setting than Euclidean space.

And the original orchard-planting problem of discrete geometry asks for a bound on the number of 3-secants of a finite set of points.