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

The relationship between a tangent and a radius at the point where they meet is that they intersect at a right angle, meaning they meet at 90 degrees. This is a fundamental property of circles in geometry. When a tangent touches a circle, it does so at exactly one point, which is known as the point of tangency. At this point, the radius drawn from the center of the circle to the point of tangency is perpendicular to the tangent line.

This relationship is important because it helps in various geometric constructions and proofs involving circles. The perpendicularity signifies that the tangent line is "flat" with respect to the radius, illustrating how the tangent does not enter the circle but instead just touches the edge. Recognizing this 90-degree angle can also assist in solving problems related to angles, triangle properties, and circle theorems effectively.