$I\left( x;y \right)$  là tâm đường tròn ngoại tiếp $\Delta MNP$

$\Leftrightarrow \left\{ \begin{align} & M{{I}^{2}}=N{{I}^{2}} \\ & M{{I}^{2}}=P{{I}^{2}} \\ \end{align} \right.$$\Leftrightarrow \left\{ \begin{align} & {{\left( x-1 \right)}^{2}}+{{\left( y+1 \right)}^{2}}={{\left( x-3 \right)}^{2}}+{{\left( y-1 \right)}^{2}} \\ & {{\left( x-1 \right)}^{2}}+{{\left( y+1 \right)}^{2}}={{\left( x-5 \right)}^{2}}+{{\left( y+5 \right)}^{2}} \\ \end{align} \right.$

$\Leftrightarrow \left\{ \begin{align} & x+y=2 \\ & x-y=6 \\ \end{align} \right.$$\Leftrightarrow \left\{ \begin{align} & x=4 \\ & y=-2 \\ \end{align} \right.\Leftrightarrow I\left( 4;-2 \right)$