The circle orthogonal to the three circles$x^2 + y^2 + a_i x + b_i y + c = 0$, (i = 1, 2, 3) is

$$\begin{gathered} \mathrm{Let} \mathrm{S}:{\mathrm{x}}^2+{\mathrm{y}}^2+2\mathrm{gx}+2\mathrm{fy}+\mathrm{c}=0 \mathrm{be} \mathrm{a} \mathrm{req}uired ci\mathrm{rcle} \\ apply the condition \\ 2{\mathrm{gg}}^1+2{\mathrm{ff}}^1=\mathrm{c}+{\mathrm{c}}^1 \\ Then required e\mathrm{quation} \mathrm{of} \mathrm{circle} \mathrm{is} {\mathrm{x}}^2+{\mathrm{y}}^2=\mathrm{c} \mathrm{which} \mathrm{cuts} \mathrm{given} \mathrm{circles} \mathrm{orthogonally} \end{gathered}$$