8 Let $\vec{i}$ and $\vec{j}$ represent the unit vectors on the $x$ and $y$ axes of a Cartesian coordinate system, respectively, and $|\vec{a}-\vec{i}|+|\vec{a}-\overrightarrow{2 j}|=\sqrt{5}$. Then the range of $|\vec{a}+\overrightarrow{2 i}|$ is ( ).
(A) $[2 \sqrt{2}, 3]$
(B) $\left[\frac{6 \sqrt{5}}{5}, 2 \sqrt{2}\right]$
(C) $[\sqrt{5}, 4]$
(D) $\left[\frac{6 \sqrt{5}}{5}, 3\right]$
$8 \mathrm{D}$ Hint: The endpoint of the vector $\vec{a}$ that satisfies $|\vec{a}-\vec{i}|+|\vec{a}-\overrightarrow{2 j}|=\sqrt{5}$ lies on the line segment $2 x+y-2=0(0 \leqslant x \leqslant 1)$, so the maximum value of $|\vec{a}+\overrightarrow{2 i}|$ is the distance between the point $(-2,0)$ and $(1,0)$, which is 3, and the minimum value is the distance from the point $(-2,0)$ to the line segment, which is $\frac{6 \sqrt{5}}{5}$.