The diameter of the circle is \(13\) cm, so the radius \(r\) is:

["Understanding Circle Geometry: How to Calculate the Radius from the Diameter", "In basic geometry, a circle is defined by its diameter and radius—two fundamental properties that help describe its size and structure. One of the most straightforward relationships in circle geometry is the connection between the diameter ((d)) and the radius ((r)): the radius is always half the diameter.", "If the diameter of a circle is given as (13) cm, finding the radius is simple and based on a clear mathematical formula. The relationship is defined by:", "[\nr = \frac{d}{2}\n]", "Substituting the given diameter:", "[\nr = \frac{13, \ ext{cm}}{2} = 6.5, \ ext{cm}\n]", "Thus, the radius of the circle is (6.5) cm.", "Understanding this basic relationship is essential not only for solving geometry problems but also for real-world applications such as engineering, architecture, and design. The diameter provides the full width across the circle, while the radius measures just half that width—making the radius a convenient unit when working with circles, especially when calculating area, circumference, or comparing to other circular elements.", "In summary, from a diameter of (13) cm, dividing by two gives the radius:\n[\nr = 6.5, \ ext{cm}\n]", "This simple yet powerful concept lies at the heart of working with circles, enabling clear and accurate calculations in both academic and practical settings."]