Gọi đường tròn tâm \(I\left(a;b\right)\Rightarrow R=\left|a\right|\)
\(\left\{{}\begin{matrix}\overrightarrow{AI}=\left(a-2;b\right)\\\overrightarrow{BI}=\left(a-4;b-2\right)\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\left(a-2\right)^2+b^2=a^2\\\left(a-4\right)^2+\left(b-2\right)^2=a^2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4a=b^2+4\\b^2-8a-4b+20=0\end{matrix}\right.\) \(\Rightarrow b^2-2\left(b^2+4\right)-4b+20=0\)
\(\Rightarrow-b^2-4b+12=0\Rightarrow\left[{}\begin{matrix}b=2\Rightarrow a=2\\b=-6\Rightarrow a=10\end{matrix}\right.\)
Có 2 đường tròn thỏa mãn: \(\left[{}\begin{matrix}\left(x-2\right)^2+\left(y-2\right)^2=4\\\left(x-10\right)^2+\left(y+6\right)^2=100\end{matrix}\right.\)
