Asked to draw a quadrilateral with sides 3, 4, 5 and 6, one might create what's shown above, using the tools available in, say geogebra. A moment's reflection indicates that the requirement would be met if CD 'connected to' AD to make this a concave figure.
I have been searching for software that would enable its user to move BC and AC in such a way that remained attached to AB yet CD's length was a constant four.
Instrumenpoche seems a possibility; however, my French in poor. I would be willing to put in the effort if it appeared that it might be able to do this.
Incidentally, this is not a graphing problem, and I haven't been able to make geogebra do it.
Somewhat like in this sketch?
Ignore the given circle through D.
Line or link CD including end points remains fixed in length while A and B move to positions A' and B' on circles (blue, yellow) with centers D,C respectively.
4-bar mechanism.