What is the name of a line segment whose endpoints lie on a circle?

A line segment whose endpoints lie on a circle is known as a chord. Chords are defined by their endpoints being located anywhere along the circumference of the circle, effectively slicing through the interior of the circle. This distinction sets chords apart from other types of line segments associated with circles, such as diameters and radii.

A diameter is a specific type of chord that passes through the center of the circle and has its endpoints on the edge of the circle. Therefore, while all diameters are chords, not all chords are diameters. A radius, on the other hand, is a segment connecting the center of the circle to a point on the circle, which means its endpoints do not both lie on the circumference. A tangent is a line that touches the circle at exactly one point and does not have endpoints on the circle.

Understanding these definitions clarifies why a chord is the correct term for any line segment whose endpoints are strictly on the circle's circumference.