If we can assume that the segments always form a cycle (the ones in your example do), then the Graph module's find_a_cycle method seems to do the trick...

use Graph;

my @AoA = (
    [11,29, 10,25],
    [15,35, 11,29],
    [15,15, 11,21],
    [10,25, 11,21],
    [15,35, 21,39],
    [25,40, 21,39],
    [21,11, 25,10],
    [15,15, 21,11],
    [35,35, 29,39],
    [29,39, 25,40],
    [35,15, 29,11],
    [25,10, 29,11],
    [40,25, 39,29],
    [35,35, 39,29],
    [39,21, 40,25],
    [35,15, 39,21],
);

my $graph = Graph::Undirected->new;

for my $pair (@AoA)
{
    my ($x1, $y1, $x2, $y2) = @$pair;
    $graph->add_edge("$x1,$y1", "$x2,$y2");
}

print "$_\n" for $graph->find_a_cycle;
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If the points are not guaranteed to form a cycle, then I think Graph is still a good place to start.