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## Main Question or Discussion Point

**Given 3 points how to find the centre and radius of a circle in 3 D??**

Say the 3 points are (a,b,c),(a1.b1,c1) and (a2,b2,c2)...

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Say the 3 points are (a,b,c),(a1.b1,c1) and (a2,b2,c2)...

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Do you mean a sphere? Are these arbitrary points anywhere in the sphere or on the surface?

- #3

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[tex]

\left|

\begin{array}{llll}

x^2+y^2 & x & y & 1 \\

x_1^2+y_1^2 & x_1 & y_1 & 1 \\

x_2^2+y_2^2 & x_2 & y_2 & 1 \\

x_3^2+y_3^2 & x_3 & y_3 & 1

\end{array}

\right|=0

[/tex]

- #4

Borek

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Three points are not enough to define the sphere. Four will do the trick (unless they will not, but you need four at least). Points inside the sphere do not belong to the sphere. IMHO question is very precise.Do you mean a sphere? Are these arbitrary points anywhere in the sphere or on the surface?

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Borek you are absolutely right. I just wanted to make sure.

- #6

mathwonk

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these three planes should meet at the center of the circle.

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