[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]By simultaneously moving parallels to two lines, with the trace activated, the color of the nearest line remains at each point, yielding the angle bisectors. In the case of three lines, we can visualize the incenter and the excenters of the triangle they determine.[br][br]As a specific case, we can visualize the [b]medial axis[/b] [url=https://en.wikipedia.org/wiki/Medial_axis][img]https://www.geogebra.org/resource/scjbyz2p/0tuzuVw455vxurEw/material-scjbyz2p.png[/img][/url] of a polygon as the boundary (composed of segments and arcs of parabolas) between the surviving traces.[br][br]Similar to before, we can also easily visualize and construct the corresponding geometric locus of the angle bisector.

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