2. A tangent to a circle is perpendicular to the radius to the point of tangency.

Let O be the center of the circle and let AF be tangent to the circle at F.

Since A, any point on the line besides F, is outside the circel, its distance to O, the center of the circle, is greater than the radius of the circle, which is the distance from O to F. This says that the distance from O to F is the shortest distance from the point O to the line, which from Theorem 1, from this section, is the perpendicular distance. We conclude that OF is perpendicular to AF.