Tangents are not real

A line that intersects only one point on a circle so that a perpendicular line could be made off that point is not possible, because the line would hit an infinite number of points on the circle before reaching just one point on the edge of the circle.  Sure you can specify one point on a circle, but the line is touching infinitely more than just one point as well as that single point.  Touch one point on a triangle, sure.  Circle, no.

Depends how large the point in question is meant to be. Is a point classified as a single atom, or a set of millions of atoms? A point could be an inch or a foot or a yard or a mile.