Cone–Cylinder Intersection and Locus Construction

This example demonstrates how geometric relationships between a cone and a cylinder can be obtained via intersection/section lines, producing a corresponding set of points (locus) that changes with the construction. It highlights core ideas from solid geometry—modeling Cone and Cylinder, defining slicing constraints, and extracting key intersection geometry—along with angle relationships (Angles, similar triangles) and trigonometric reasoning (Sinus) that can be connected to equations. Construction-wise, GeoGebra commands such as Point, Circle, Intersect, Segment build foundational objects and intersection points; Cone and Cylinder create the 3D solids; Line and OrthogonalPlane establish the spatial cutting/constraint setup; PointIn filters points with respect to constructed geometric conditions; and Locus generates the point sets (e.g., multiple locus objects) to visualize how the solution set evolves. Suitable for upper secondary and early university students learning 3D geometry, geometric construction, and linking constructions to equation/functional descriptions.