A triangle is formed by the lines whose combined equation is given by (x+y-4)(x y-2 x-y+2)=0. The equation of its circumcircle is

$\begin{array}{l}(\mathrm{x}+\mathrm{y}-4)(\mathrm{xy}-2\mathrm{x}-\mathrm{y}+2)=0\\ (\mathrm{x}+\mathrm{y}-4)(\mathrm{x}-1)(\mathrm{y}-2)=0\because \mathrm{AB}\perp \mathrm{AC}\end{array}$

therefore B C  is diameter, then equation of circumcircle is 

$\Rightarrow (\mathrm{x}-2)(\mathrm{x}-1)+(\mathrm{y}-2)(\mathrm{y}-3)=0$

$\Rightarrow {\mathrm{x}}^2+{\mathrm{y}}^2-3\mathrm{x}-5\mathrm{y}+8=0$