[color=#999999]This activity belongs to the [i]GeoGebra book[/i] [url=https://www.geogebra.org/m/sw2cat9w]GeoGebra Principia[/url].[/color][br][br][br]When contracting T-circles with the trace activated, at each point in the plane the color corresponding to the nearest center survives.[br][br]With multiple points, we can visualize the Voronoi diagram and compare it with the one corresponding to the Euclidean distance.[br][br]To analyze the equidistance point-line, we need to determine the distance from a point (x, y) to a line r: a x + b y + c = 0. This distance is ([b]this formula is provided to students[/b] and can be directly introduced in the algebraic view): [br][br] [color=#CC3300]Xr(x,y) = |a x + b y + c| / Max(|a|, |b|)[/color][br]  [br]From the point-line equidistance the T-parabola arises, while from the point-circle equidistance the T-ellipse and the T-hyperbola emerge.[br][br]If we consider equidistance to the sides of a polygon, its skeleton and median axis arise. We can traverse it with a bitangent disk to verify this.[br][br]Finally, we can also find the T-equidistant path between two curves, either through offset (as shown here) or by generating a heat map.[br][list][*]Note: For a better view of the construction, it is recommended to download the ggb file [url=https://www.geogebra.org/material/download/format/file/id/qpzdxu88]here[/url].[/*][/list]

[br][color=#999999]Author of the construction of GeoGebra: [url=https://www.geogebra.org/u/rafael]Rafael Losada[/url].[/color]