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This is inspired from this recent question. Given in the plane a tree-linkage (fixed length rigid edges, vertices are flexible joints, connected and no cycles) is there a simple description of when the area of its convex hull is maximal? Or alternatively an algorithm to find this maximal configuration? I think I checked the following simple cases:

In the case when we have three edges connected at a point (say the edges are $OA,OB,OC$). Then the maximal area is achieved when $O$ is the orthocenter of $ABC$.

In the case when we have a free path $A_1,A_2,\dots,A_n$ the maximal area of the convex hull is attained when all the vertices lie on the circle with diameter $A_1A_n$.

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I guess that the cyclic orders of edges around vertices are also prescribed? – Roland Bacher Apr 30 '10 at 15:06

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