Well, there is a lot to say about "tangent".
For example, it has a trigonometric meaning = sinus(x) divided by cosinus(x)... But how can I show the true meaning without a drawing?

Also, about a line tangent to a given curve, say for example a circle.. Take two points on the circle, and draw the line between themselves. This is a secant line. Then, think of the two points as approaching more and more between themselves...that line moves, and at the limit of the process it becomes the tangent line - you can say that it intersect the circle in two coincident points......And..... stop me..... this is my field...