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