Angles in Circles: Exploring Inscribed and Central Angles

①This interactive GeoGebra example demonstrates the relationships among angles formed inside a circle, such as central angles, inscribed angles, and angles formed by intersecting chords, showing how they relate to intercepted arcs. ②Core mathematical concepts include circle geometry, the inscribed angle theorem, the central angle theorem, and the arc-angle correspondence, which are fundamental for geometric proofs and problem-solving. ③Construction details: using GeoGebra commands Circle to create circle c, Point to place center O and points A, B, C on the circumference, Segment to draw chords and radii, and Angle to label angles α and β, with text1 and text2 displaying measured values, resulting in a dynamic and adjustable figure. ④This resource is suitable for middle and high school geometry classes, ideal for classroom demonstrations, student exploration of circle angle properties, and as an introductory exercise in geometric construction and dynamic verification.