110 If $x, y$ satisfy $4 x^{2}=8-y^{2}$, then the minimum value of $\sqrt{x^{2}+(y-3)^{2}}+\sqrt{(x-2)^{2}+(y-1)^{2}}$ is $\qquad$
$1102 \sqrt{2}$. Let point $A$ have coordinates $(2,1)$, and point $B$ have coordinates $(0,3)$. Find the minimum value of the sum of the distances from any point on the ellipse
$$
\frac{x^{2}}{2}+\frac{y^{2}}{8}=1
$$

to points $A$ and $B$.
The equation of line $AB$ is
$$
y=-x+3,
$$

It is easy to see that segment $AB$ intersects the ellipse at two points $C(1,2)$ and $D\left(\frac{1}{5}, \frac{14}{5}\right)$. Therefore, the minimum value is the length of $AB$, which is $2 \sqrt{2}$.