The radius of a circle is ______ to a tangent at the point of tangency.

The radius of a circle is perpendicular to a tangent at the point of tangency, which is a fundamental concept in geometry. This means that when a tangent line touches the circumference of a circle, it does so at only one point, known as the point of tangency. At this precise location, the radius drawn from the center of the circle to the point of tangency meets the tangent line at a right angle (90 degrees).

This relationship is critical in various applications, including construction and surveying, where understanding the properties of curves and lines is essential for accurate measurements and designs. The perpendicularity ensures that the tangent line does not intersect the circle anywhere else and helps in defining the geometric properties of circles that are vital in surveying calculations, like determining the curvature or creating arcs.

The other terms presented in the options do not accurately describe the relationship between the radius and the tangent. The radius cannot be either parallel, diagonal, or simply another tangent, since each of these terms describes different geometric relationships that do not apply to the scenario involving a radius and tangent.