This activity belongs to the GeoGebra book GeoGebra Principia. If we input XA + XB = XC, the resulting locus corresponds to the intersection of a family of ellipses XA + XB = k and a family of circles XC = k as the parameter k varies. In the case of four points, XA + XB = XC + XD corresponds to the intersection of two families of ellipses.

• Note: Calculating the minimum and maximum values of k that ensure intersection is not straightforward. An approach can be seen in [6].

The case XA + XB = Xr is also presented, along with the representation of the corresponding algebraic equations.