[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]If we input XA + XB = XC, the resulting locus corresponds to the intersection of a family of ellipses [br][br] XA + XB = k [br][br]and a family of circles[br][br] XC = k[br][br]as the parameter k varies.[br] [br]In the case of four points, XA + XB = XC + XD corresponds to the intersection of two families of ellipses.[br][list][*][color=#808080]Note: Calculating the minimum and maximum values of k that ensure intersection is not straightforward. An approach can be seen in [[url=https://www.geogebra.org/m/sw2cat9w#material/er8nf4qt]6[/url]].[/color][br][/*][/list]The case XA + XB = Xr is also presented, along with the representation of the corresponding algebraic equations.

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