Tangent Lines and Secant Lines

(This is about lines, you might want the tangent and secant functions)

Secant (line)

 

A tangent line just touches a curve at a point, matching the curve's slope there. (From the Latin tangens "touching", like in the word "tangible".)

A secant line intersects two or more points on a curve. (From the Latin secare "cut or sever")

They are lines, so extend in both directions infinitely.

Circle

On a circle they look like this:

circle lines

There are three theorems of interest here: