Between 0 to 9

Geometry Level 4

Let \(a, b, c\) be sides of a (non-degenerate) triangle satisfying \(a^2 + b^2 + c^2 = 6\). Let \(S\) be the set of all integers that can be the value of \(ab + bc + ca\). What is the arithmetic mean of the elements in \(S\)?

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