Kariya Point and Feuerbach Hyperbola Visualization

This GeoGebra example demonstrates how to locate the Kariya point within a triangle-related configuration and how to visualize its geometric locus, forming the Feuerbach hyperbola. It centers on core concepts such as triangle centers and notable points (TriangleCenter), constructing nearest-point relationships (ClosestPoint), using circles and intersections (Circle, Intersect, Line), and producing point sets via locus and conic construction (Locus, Conic). Key construction elements include building the initial polygon/triangle and segments (Polygon, Segment, Midpoint), enforcing ratio and symmetry constraints using affine ratios and reflections (AffineRatio, Mirror), and generating the locus under parameter variation (Locus). Finally, conic-related construction steps (Conic), together with intersection and radius-based geometry (Intersect, Radius), help render the Feuerbach hyperbola and the associated marked points. Suitable for secondary-level Olympiad geometry, and for undergraduate geometry/coordinate-geometry instruction and exploratory learning.