What is a tangent line in relation to a circle?

A tangent line in relation to a circle is defined as a line that touches the circle at exactly one point. This unique interaction means that the tangent line does not cross into the circle; instead, it is perfectly aligned with the circle at that single point of contact, which is referred to as the point of tangency. This characteristic of a tangent line is fundamental in geometry, as it establishes a key relationship between the radius of the circle and the tangent line itself; the radius drawn to the point of tangency is perpendicular to the tangent line. Therefore, the concept of a tangent line is essential in various geometry applications, including constructions and proofs involving circles.