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If an external intersection is considered an intersection, then see line 1.
If not, but a tangent at a boundary point is considered an intersection, then see line 2.

If that's also not the case, it's impossible. Why? Because if we draw several connecting segments through a line and then try to connect the beginning of the first segment with the end of the last, regardless of the segments themselves, we have two options:
1. The connection of the segments lies on one side of the original line (and does not intersect it).
2. The connection of the segments intersects the line, but also intersects other segments, which does not create a polygon. Why does it intersect? Well, here the level of abstraction becomes even more complex. If necessary, I will try to finish the reasoning.