Cauchy–Goursat Theorem Example: Geometry Construction with a Circle and Tangent

This GeoGebra example illustrates how the Cauchy–Goursat theorem can be visualized and checked within a geometric configuration involving a circle and a tangent line. The key mathematical ideas are circle geometry (including circumscripted/circumscribed circle-type relations), tangent properties at the contact region, and the way the theorem’s conditions manifest through constrained intersection relationships. In the construction, the main workflow comes from the provided construction summary: the command "Intersect" is used to compute the essential intersection points among the given geometric objects (e.g., C, a, D, A, B, pic1, eq1). Those computed intersections then determine the relationships needed to demonstrate the theorem in a concrete diagram. Suitable for advanced high-school learners, coordinate/geometry construction practice, and early university-level instruction focused on connecting theorem statements to interactive geometric validation.