This applet shows GeoGebra's animation possibilities by using fast real-time Gröbner basis computations.[br][br]After constructing a triangle, the command [code]LocusEquation[a+b==5,C][/code] was used. For technical reasons the point [i]A[/i] is not attached to line [i]f[/i], but the slider [i]d[/i] conducts the animation by explicitly setting the [i]x[/i]-coordinate of [i]A[/i].[br][br]Note that the geometrical solution should be an ellipse with foci [i]A[/i] and [i]B[/i] in such cases when [i]c[/i]<5, because the triangle inequality ensures [i]a[/i]+[i]b[/i]>c, so there is room for possible solutions. Otherwise, if [i]c[/i]=5, we obtain [i]a[/i]+[i]b[/i]=[i]c[/i], that is [i]C[/i] must lie on the segment [i]AB[/i]; actually in this case the line [i]AB[/i] will be shown in GeoGebra because no further restrictions can be achieved by using the Gröbner basis approach. (In other words: the line is algebraically a necessary, but geometrically not-sufficient condition.) Finally, if [i]c[/i]>5, by using the triangle inequality again, we should not find any solutions, but GeoGebra delivers a hyperbola with foci [i]A[/i] and [i]B[/i]: the reason here is that there is no way in the Gröbner basis approach to exclude the hyperbola which is algebraically a necessary condition.