[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]Now we just have to use those simple tools to investigate a wide variety of situations with their assistance.[br][br]From now on, we consider the distances from an arbitrary point [b]X(x,y)[/b] to [b]A[/b] and [b]B[/b] defined as:[br][br] [color=#CC3300]XA(x,y):= Distance(X, A)[/color][br][br] [color=#CC3300]XB(x,y):= Distance(X, B)[/color][br]  [br]to a line [b]r[/b] as:[br][br] [color=#CC3300]Xr(x,y):= Distance(X, r)[/color][br]  [br]and to a circle [b]c[/b] as:[br][br] [color=#CC3300]Xc(x,y):= Distance(X, c)[/color][br][br][br][color=#CC3300][b]Equidistance to Two or Three Points[/b][/color][br][br]By contracting the circles with the activated trace, at each point in the plane, the color of the nearest center remains, resulting in the perpendicular bisector.[br][br]The implicit curve of the [b]perpendicular bisector[/b] of AB is given by the equation: [br][br] [color=#CC3300]XA – XB = 0[/color][br]  [br]In the case of three points, we can visualize the circumcenter [[url=https://www.geogebra.org/m/sw2cat9w#material/er8nf4qt]2[/url]] of the triangle they form.

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