Inscribed Angles in a Circle: GeoGebra Construction & Verification

This example demonstrates the key geometric behavior of inscribed angles: when two points on a circle define a chord and the inscribed angle is formed at a third point on the circle, the angle remains tied to the intercepted arc (or corresponding chord) even as the configuration moves. It focuses on the Inscribed Angle Theorem, the relationship between angles and circle arcs, and using construction to measure and compare angle values. Construction details in GeoGebra include: Circle to create the reference circle; Line to draw supporting lines (e.g., forming chords/structures); Intersect to obtain intersection points between lines and the circle (key points such as A, Q_1, C, etc.); CircleArc to highlight the intercepted arc that determines the angle relationship; Point and Segment to place and connect the relevant geometric objects; and Angle to compute/display the inscribed angles (e.g., α, β) for dynamic verification. Suitable for middle and high school geometry, classroom demonstrations, and interactive self-study of circle-angle properties.