3点を通る円
\[
x^{2}+y^{2}-\frac{1}{x_{1}y_{2}+y_{1}x_{3}+x_{2}y_{3}-x_{1}y_{3}-y_{1}x_{2}-y_{2}x_{3}}\left(\begin{array}{ccc}
x & y & 1\end{array}\right)\left(\begin{array}{ccc}
y_{2}-y_{3} & y_{3}-y_{1} & y_{1}-y_{2}\\
x_{3}-x_{2} & x_{1}-x_{3} & x_{2}-x_{1}\\
x_{2}y_{3}-y_{2}x_{3} & y_{1}x_{3}-x_{1}y_{3} & x_{1}y_{2}-y_{1}x_{2}
\end{array}\right)\left(\begin{array}{c}
x_{1}^{\;2}+y_{1}^{\;2}\\
x_{2}^{\;2}+y_{2}^{\;2}\\
x_{3}^{\;2}+y_{3}^{\;2}
\end{array}\right)=0
\]