Circumference that goes through 3 given points
Find the circumference that goes through points $a=(2,0)$, $b=(2,3)$ and $c=(1,3)$.
We replace them in the general equation of the circumference $x^2+y^2+Ax+By+C=0$. Thereby we obtain:
$$\left\{\begin{array}{c} 2^2+0+2A+0+C=0 \\ 2^2+3^2+2A+3B+C=0 \\ 1^2+3^2+A+3B+C=0 \end{array}\right\} \Rightarrow \left\{\begin{array}{c} 4+2A=-C \\ 13+2A+3B+C=0 \\ 10+A+3B+C=0 \end{array}\right.$$ We solve the system and get: $$\left\{\begin{array}{c} A=-3 \\ B=-3 \\ C=2 \end{array}\right.$$ And we have the equation $$x^2+y^2-3x-3y+2=0$$
$x^2+y^2-3x-3y+2=0$