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Minimize total area bounded by $N$ lines in general position

Suppose we have $N$ lines in general position (any two lines, but no three lines, meet at a point) ($N\geq 3$). Let the smallest bounded region have area $1$. Determine the minimum (or possibly infim …
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Minimize total area bounded by $N$ lines in general position

I wound up contacting Dr. János Pach (an expert in relevant fields) regarding the problem on the recommendation of my first professor. Apparently the problem (originally in a slightly different form) …
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