When a line is tangent to a circle, what relationship does it have with the radius to the point of tangency?

When a line is tangent to a circle, it intersects the circle at exactly one point, known as the point of tangency. At this specific point, the tangent line has a unique relationship with the radius that extends from the center of the circle to the point of tangency. This relationship is characterized by the fact that the tangent line is always perpendicular to the radius at the point where they meet.

This means that if you were to draw the radius to the point of tangency and then draw the tangent line at that point, the angle formed between the radius and the tangent line would be 90 degrees. This perpendicular relationship is fundamental in geometry and is used in various applications involving circles, such as in calculations related to angles, distances, and geometric proofs. The reason this relationship holds true stems from the definition of a tangent line, which is designed to "just touch" the circle without crossing it, creating a right angle with the radius at the point of contact.