What is the relationship between the radius and the tangent at the point of contact?

At the point where a radius meets the tangent line of a circle, they are always perpendicular to each other. This means that if you draw a radius from the center of the circle to the point of contact and then draw a tangent line at that same point, the angle formed between the radius and the tangent line is always 90 degrees.

This relationship is a fundamental property of circles and can be demonstrated through geometric proofs or constructions. The reason for this perpendicularity is that the tangent line is defined as a line that touches the circle at only one point and does not cross it, which inherently requires that the shortest distance (the radius) from the center of the circle to the tangent line is perpendicular.

Understanding this concept is essential in geometry, particularly when analyzing properties of circles in greater detail, such as in the study of angles, segments, and other tangential properties.