# Tangent as a Special Case of Secant

We have seen that a secant for a circle intersects the circle in two points. Let L be a secant to a circle S which intersects S at A and B. What would happened if A and B were really close to each other? In the following figure, the position of A is fixed, but B is *moved* and brought closer and closer to A. What happens to the secant L?

Different positions of the moving point B have been marked with different subscripts: B_{1}, B_{2}, and so on. As this point comes closer to A, note how the secant *comes closer and closer* to the tangent at A. Let us zoom in on the region around A. We have highlighted the tangent at A. Note how the secant approaches the tangent as B approaches A:

Thus (and this is really important): *we can think of a tangent to a circle as a special case of its secant, where the two points of intersection of the secant and the circle coincide.* This insight will prove to be really useful when you study the subject of Calculus in higher classes.