Okay: the tangent line is a line whose slope is equal to the slope of a function at a certain point. Think of an eight foot long 2 X 4 placed on or under a specific part of a small Ferris wheel or huge Hula hoop. Something like this:

(Source.)

AC would be the "2 x 4". It's the tangent.

Intuitively, we know that there are two places where the "2 x 4" would be horizontal: i.e., have a slope of zero. Flat. :)

But it is hard to justify because the circle has no edges.