Secants Intersection Outside: Exploring the External Secant Theorem

①This example demonstrates the geometric configuration of two secants drawn from an external point to a circle, intersecting the circle at four points, and illustrates the relationship between the external point and the intersection points, namely the secant theorem (external power theorem). ②Core mathematical concepts include secants of a circle, external intersection point, equality of products of segment lengths (PA·PB = PC·PD), symmetry, and angle relationships. ③Construction highlights: using GeoGebra commands such as Circle, Point, Line, Rotate, Angle, Intersect, Segment, and LineBisector to construct the circle, external point, two secants, and their intersection points; angles are labeled via the Angle tool, and line bisectors are used to analyze symmetry. ④Suitable for high school geometry or introductory college geometry courses, providing an interactive way to understand the power of a point theorem and to dynamically explore the invariance of the product of segment lengths as the secants vary.