Interactive Circle Terminology: Tangent, Secant, and Circumcircle

This example uses interactive manipulation to demonstrate how common circle terminology corresponds to concrete geometric elements and their spatial relationships. It focuses on key concepts such as circle components, chords and secant lines, tangents and their tangency points, circle arcs, and the circumcircle/circumscribed circle terminology. Construction in GeoGebra highlights: using Circle to create the circle, Segment and Point/PointIn to define points and point membership, and Line to form straight lines; then Intersect is used to compute intersection points between lines (secants/tangents) and the circle. Tangent directly generates tangency behavior, while CircleArc constructs arc elements, and Rotate can illustrate how the configuration changes under rotation while preserving the terminology. The scene is organized from multiple labeled points (e.g., A, B, C, D, etc.) together with derived lines, arcs, and circle objects. Suitable for middle and high school geometry instruction, self-study, and classroom demonstrations aimed at recognizing terms, practicing constructions, and building intuitive understanding of circle properties.