Ratio of Central Angle & Inscribed Angle of the Same Arc

①This interactive GeoGebra example demonstrates the relationship between the central angle (red) and the inscribed angle (blue) subtending the same arc of a circle.②The core mathematical concept is the Inscribed Angle Theorem: the inscribed angle is exactly half the central angle when both intercept the same arc.③Construction details: using GeoGebra commands such as Circle to define the circle, Point to create movable points A, B, C, D, Segment to draw chords, Angle to measure the central angle α and inscribed angle β, and a computed ratio RatioRedDividedByBlue displayed via text1 to show the constant value 2.④This resource is suitable for middle school geometry lessons or high school review, helping students visualize and verify the theorem through dynamic manipulation, and fostering inductive reasoning and geometric intuition.