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
