Distance from $(1,1,0)$:

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• Let’s find $(x, y, z)$ such that its distance to each of the three points is also $\sqrt{2}$:
• Distance from $(0,0,0)$:
• x^2 + y^2 + z^2 = 2
• \Rightarrow x^2 - 2x + 1 + y^2 - 2y + 1 + z^2 = 2
• \Rightarrow (x^2 + y^2 + z^2) - 2x - 2y + 2 = 2
• \Rightarrow 2 - 2x - 2y + 2 = 2 \Rightarrow -2x - 2y = -2 \Rightarrow x + y = 1

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