Jerabek Hyperbola: A Special Conic Associated with a Triangle's Circumcenter and

This example demonstrates the complete construction of the Jerabek Hyperbola, a special conic related to a triangle's circumcircle, orthocenter, and conjugate points. The core mathematical concepts involve the circumcenter, orthocenter, circumcircle, angle bisectors, orthogonal lines, and the generation of a conic (hyperbola). Construction highlights: using GeoGebra commands such as Line, Circle, Center, OrthogonalLine, Intersect, Point, AngularBisector, Mirror, Polygon, Midpoint, and Conic, the triangle ABC, its circumcircle c, and orthocenter H are built, followed by a series of auxiliary points (D, E, F, G, K, etc.) and mirror/midpoint operations, finally yielding the Jerabek hyperbola via the Conic command. This example is suitable for high school and above students or math enthusiasts, offering deep insight into the interplay between conic sections and triangle geometry, and serving as an excellent resource for dynamic geometry exploration.