The ray emanating from an external point toward a circle intersects the circle at two points. The segment connecting the external point to the farthest intersection point along the ray, measured from the external point, constitutes the external segment. Its length is a key factor in several geometric theorems related to intersecting secants and tangents.
Understanding the properties of this segment is vital in solving problems related to circle theorems and geometric constructions. Historically, the relationships involving these segments have been foundational in the development of geometric principles and continue to find application in fields like surveying, architecture, and computer graphics. They allow indirect measurement and facilitate calculation where direct measurement is impractical.