Circumscribed (Tangent-Tangent) Angles: Exploring Angles Formed by Two Tangents

This GeoGebra example demonstrates the geometric properties of circumscribed (tangent-tangent) angles formed by two tangents drawn from an external point to a circle. The core mathematical concepts include tangent properties, the relationship between the tangent-tangent angle and the intercepted arc, and angle measurement. The construction uses commands such as Circle to create the circle, Tangent to draw two tangents from an external point, Intersect to find tangent points, Segment to connect points, Distance to measure lengths, Angle to measure the angles α and β, and Text to display distance and angle values. This example is suitable for upper middle school or high school students to intuitively understand the tangent-tangent angle theorem, and can also serve as a dynamic geometry exploration by dragging the external point to observe how the angles change.