Najpierw wyznaczymy wierzchołki trójkąta mając dane proste zawierające jego boki.

Wierzchołek A

$\{\begin{array}{l}y=3x-9\\ 2x+y-1=0\end{array}$  

$\{\begin{array}{l}y=3x-9\\ 2x+3x-9-1=0\end{array}$  

$\{\begin{array}{l}y=3x-9\\ 5x-10=0\mid +10\end{array}$  

$\{\begin{array}{l}y=3x-9\\ 5x=10\mid :5\end{array}$  

$\{\begin{array}{l}y=3x-9\\ x=2\end{array}$  

$\{\begin{array}{l}y=3\cdot 2-9\\ x=2\end{array}$

$\{\begin{array}{l}y=6-9\\ x=2\end{array}$

$\{\begin{array}{l}y=-3\\ x=2\end{array}$

$A=\left(2,-3\right)$

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Wierzchołek B

$\{\begin{array}{l}y=-x+3\\ 2x+y-1=0\end{array}$  

$\{\begin{array}{l}y=-x+3\\ 2x-x+3-1=0\end{array}$  

$\{\begin{array}{l}y=-x+3\\ x+2=0\mid -2\end{array}$  

$\{\begin{array}{l}y=-x+3\\ x=-2\end{array}$  

$\{\begin{array}{l}y=-\left(-2\right)+3\\ x=-2\end{array}$  

$\{\begin{array}{l}y=5\\ x=-2\end{array}$  

$B=\left(-2,5\right)$  

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Wierzchołek C

$\{\begin{array}{l}y=-x+3\\ y=3x-9\end{array}$  

$\{\begin{array}{l}3x-9=-x+3\mid +x+9\\ y=3x-9\end{array}$  

$\{\begin{array}{l}4x=12\mid :4\\ y=3x-9\end{array}$  

$\{\begin{array}{l}x=3\\ y=3x-9\end{array}$  

$\{\begin{array}{l}x=3\\ y=3\cdot 3-9\end{array}$  

$\{\begin{array}{l}x=3\\ y=0\end{array}$  

$C=\left(3,0\right)$  

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Równanie ogólne okręgu

$x^2+y^2-2ax-2by+c=0$  

Po podstawieniu kolejno współrzędnych punktów A, B i C do równania okręgu otrzymamy układ trzech równań

$\{\begin{array}{l}{2}^2+{\left(-3\right)}^2-2a\cdot 2-2b\cdot \left(-3\right)+c=0\\ {\left(-2\right)}^2+5^2-2a\cdot \left(-2\right)-2b\cdot 5+c=0\\ 3^2+0^2-2a\cdot 3-2b\cdot 0+c=0\end{array}$  

$\{\begin{array}{l}4+9-4a+6b+c=0\\ 4+25+4a-10b+c=0\\ 9-6a+c=0\mid +6a-9\end{array}$  

$\{\begin{array}{l}13-4a+6b+c=0\\ 29+4a-10b+c=0\\ c=6a-9\end{array}$  

$\{\begin{array}{l}13-4a+6b+6a-9=0\\ 29+4a-10b+6a-9=0\\ c=6a-9\end{array}$  

$\{\begin{array}{l}4+6b+2a=0\mid :2\\ 20+10a-10b=0\mid :10\\ c=6a-9\end{array}$  

$\{\begin{array}{l}2+3b+a=0\\ 2+a-b=0\mid +b\\ c=6a-9\end{array}$  

$\{\begin{array}{l}2+3b+a=0\\ b=2+a\\ c=6a-9\end{array}$  

$\{\begin{array}{l}2+3\left(2+a\right)+a=0\\ b=2+a\\ c=6a-9\end{array}$  

$\{\begin{array}{l}2+6+3a+a=0\\ b=2+a\\ c=6a-9\end{array}$  

$\{\begin{array}{l}8+4a=0\mid -8\\ b=2+a\\ c=6a-9\end{array}$  

$\{\begin{array}{l}4a=-8\mid :4\\ b=2+a\\ c=6a-9\end{array}$  

$\{\begin{array}{l}a=-2\\ b=2-2\\ c=6\left(-2\right)-9\end{array}$  

$\{\begin{array}{l}a=-2\\ b=0\\ c=-12-9\end{array}$  

$\{\begin{array}{l}a=-2\\ b=0\\ c=-21\end{array}$  

Równanie okręgu

$x^2+y^2+4x-21=0$  

$x^2+y^2+4x+4-25=0$  

${\left(x+2\right)}^2+y^2=25$