A Trophy-Style 3D Geometry Construct from Circle and Tangent Relations (v2)

This GeoGebra example demonstrates how plane circle-and-tangent geometry can be transformed into a trophy-like 3D solid by combining arcs, polygons, intersections, and rotational surface generation. The central math ideas include unit-circle geometry, the geometric meaning behind the tangent-function (as reflected by tangency-related constructions), circle arcs/ circumcircle-arc handling, and boundary creation via intersecting solids and surfaces. Construction highlights: Polygon is used to build key profile regions (points such as A, B, C, D), while Prism and Cylinder provide the 3D building blocks; Point defines control and anchor points (including q1, q2 and parameterized points like e, f, g, h, j, as well as the many vertices/edge points). Intersect refines the shape by cutting where solids/surfaces meet, Rotate creates the swept/assembled geometry, CircumcircleArc supplies the arc segments used in the enclosure, and Surface produces the final curved faces (with named objects like face* and edge* supporting the model’s structure). Suitable for high school to early undergraduate audiences for geometry construction, solid geometry visualization, and connecting unit-circle/trigonometric ideas to 3D modeling.