Tangents

I used to get really mindfucked by tangents.  How can a line intersect with a point on a circle to form a ninety degree angle with the line only touching one point?  A circle is made of an infinite number of points.  Points have no width or height.  How can a line hit only one exact point on the circle without brushing into an infinite number of points right next to it that make up its curve?

Think of it like the Pauli exclusion principle,


lol wut