# 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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