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# Puzzles

## Balanced sets

A set of points in the plane is called 'balanced' if for any two points $$A$$ and $$B$$ in the set, there is another point $$C$$ in the set such that $$AC=BC$$ (here $$AC$$ is the distance between $$A$$ and $$C$$).
For all $$n\geq3$$, find a balanced set of $$n$$ points.
If you enjoyed this puzzle, check out Sunday Afternoon Maths XLIV,
puzzles about coordinates, or a random puzzle.

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