Mặt cầu đi qua bốn điểm Aleft( 2;2;2 right), Bleft( 4;0;2 right), Cleft( 4;2;0

Gọi $I\left( {a;b;c} \right)$, khi đó ta có $\left\{ \begin{array}{l}
I{A^2} = I{B^2}\\
I{A^2} = I{C^2}\\
I{A^2} = I{D^2}
\end{array} \right.$
$ \Leftrightarrow \left\{ \begin{array}{l}
{\left( {2 - a} \right)^2} + {\left( {2 - b} \right)^2} + {\left( {2 - c} \right)^2} = {\left( {4 - a} \right)^2} + {b^2} + {\left( {2 - c} \right)^2}\\
{\left( {2 - a} \right)^2} + {\left( {2 - b} \right)^2} + {\left( {2 - c} \right)^2} = {\left( {4 - a} \right)^2} + {\left( {2 - b} \right)^2} + {c^2}\\
{\left( {2 - a} \right)^2} + {\left( {2 - b} \right)^2} + {\left( {2 - c} \right)^2} = {\left( {4 - a} \right)^2} + {\left( {2 - b} \right)^2} + {\left( {2 - c} \right)^2}
\end{array} \right.$
$ \Leftrightarrow \left\{ \begin{array}{l}
4 - 4a + 4 - 4b = 16 - 8a\\
4 - 4a + 4 - 4c = 16 - 8a\\
4 - 4a = 16 - 8a
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = 3\\
b = 1\\
c = 1
\end{array} \right. \Rightarrow I\left( {3;1;1} \right).$