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I came across an interesting question online that was about vertices of quadrilaterals. I am still stumped as to how to find the answer of this solution.

The question I found was:

Is it possible to find 4 points that are the vertices of 2 different convex quadrilaterals? If so, what is the maximum number of convex quadrilaterals that can have the same set of vertices?

I do not think that it is possible to find 4 points that are the vertices of 2 different convex quadrilaterals, but I am not sure if what I think is wrong or right? If my conclusion is right, could someone explain why please?

Thank you very much.

Michael Silva

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The only convex quadrilateral with this vertices may be defined as intersection of all convex sets containing them. So the answer is 1.

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