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Home » Taking the square root of both sides, we find: - Appcentric

Taking the square root of both sides, we find: - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \text{Distance between } (1,1,0) \text{ and } (1,0,1): \sqrt{0 + (1)^2 + (1)^2} = \sqrt{2}

📌 So all edges are of length $\sqrt{2}$.

📌 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

📌 Distance from $(1,1,0)$:

📌 \Rightarrow x^2 - 2x + 1 + y^2 - 2y + 1 + z^2 = 2

📌 \Rightarrow (x^2 + y^2 + z^2) - 2x - 2y + 2 = 2

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