Do I thuộc d nên tọa độ có dạng: \(I\left(a;-2a+1\right)\)
\(\left(C\right)\) tiếp xúc \(\Delta_1;\Delta_2\Rightarrow d\left(I;\Delta_1\right)=d\left(I;\Delta_2\right)=R\)
\(\Rightarrow\dfrac{\left|3a+4\left(-2a+1\right)-1\right|}{\sqrt{3^2+4^2}}=\dfrac{\left|4a+3\left(-2a+1\right)-8\right|}{\sqrt{4^2+3^2}}\)
\(\Leftrightarrow\left|5a-3\right|=\left|2a+5\right|\Rightarrow\left[{}\begin{matrix}5a-3=2a+5\\5a-3=-2a-5\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}a=\dfrac{8}{3}\\a=-\dfrac{2}{7}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}I\left(\dfrac{8}{3};-\dfrac{13}{3}\right)\\I\left(-\dfrac{2}{7};\dfrac{11}{7}\right)\end{matrix}\right.\)
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