Circle Theorem 3: Tangent and Chord Angle Relationships

This GeoGebra example demonstrates the geometric relationships defined by Circle Theorem 3, focusing on the angles formed by tangents, chords, and vertices on a circle. The core mathematical concepts include the angle between a tangent and a chord, inscribed angles, and cyclic geometric configurations. To construct this visual model, the `Circle` command is used to define the primary circle, while `Tangent` and `Segment` commands draw the necessary lines and chords. `Point` objects are placed at key intersections, and `Polygon` is used to highlight geometric regions. The `Angle` command dynamically measures α, β, γ, and δ, providing visual proof of the theorem's constant relationships. It is highly suitable for secondary school geometry lessons, flipped classroom environments, and interactive math labs.