Conjecturing about Inscribed Angles of Circles

① This dynamic geometry example demonstrates the relationship between an inscribed angle (vertex on the circle, sides intersecting the circle) and the central angle subtending the same arc, guiding learners to observe and conjecture that the inscribed angle is half the central angle. ② Core mathematical concepts include the Inscribed Angle Theorem, arcs, central angles, inscribed angles, angle measurement and comparison, along with foundational geometry such as triangle angle sums and isosceles triangle properties. ③ Construction highlights: Based on the construction summary, GeoGebra commands such as Polygon, Angle, LineBisector, Intersect, Circle, and Segment are used to create circle c, points A, B, C, angles α and β, and other objects; a button (button1) and text (text1) enable interactive conjecture and verification, possibly with a boolean variable (bool) controlling display. ④ Suitable for upper middle school or lower high school students learning plane geometry, and useful for teachers demonstrating or students independently exploring the inscribed angle theorem, fostering inductive reasoning from specific cases to general principles.