Lengths in Circles: Secant and Tangent

①This example demonstrates the geometric relationship between the lengths of a secant and a tangent drawn from an external point to a circle, visually illustrating the tangent-secant power theorem. ②Core mathematical concepts include tangent lines, secant lines, the power of a point, similar triangles, and proportional segment lengths, emphasizing that the square of the tangent length equals the product of the secant's external and total segments. ③Construction details: using GeoGebra commands such as Circle, Point, Segment, Intersect, Distance, and Tangent, the construction creates a circle c, an external point P, a tangent point E, and secant intersections D and C, then measures lengths like ED, EC, and EB; dragging P dynamically updates the values. ④Suitable for high school geometry classes or self-study, this interactive model helps verify the circle power theorem and serves as a dynamic geometry teaching resource.