Given 4 points $A$, $B$, $C$ and $D$ in general position in the euclidean plane, is it possible to determine from the 6 distances $AB$, $BC$, $CD$, $AD$, $AC$ and, $BD$ alone, whether every point is a corner of their convex hull under the restriction that comparing sums and/or differences of the distances is the only allowed operation and that no information about the point's coordinates is available.

Background of the question is whether it is possible to generalize the concept of intersection to non-adjacent edges of a general weighted graph. If the answer were affirmative, then geometric concepts like inside/outside relations or convex hulls would be an "intrinsic" property of graphs; triangulations of complete graphs would then also be more flexible and could contain complete subgraphs of order 4.