2 Let $C$ be a circle with radius $r$, centered at the point $(\sqrt{2}, \sqrt{3})$, where $r$ is a positive real number. When $x, y$ are both rational numbers, the point $(x, y)$ is called a rational point. The maximum number of rational points on circle $C$ is
A. 0
B. 1
C. 2
D. 3
2 B Take a rational point $A$ arbitrarily. Draw a circle passing through $A$ with center at $(\sqrt{2}, \sqrt{3})$, then there is at least one rational point on the circle. If there are two rational points $\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right)$, then the perpendicular bisector of the line segment connecting these two points is
$$
\left(x-x_{1}\right)^{2}+\left(y-y_{1}\right)^{2}=\left(x-x_{2}\right)^{2}+\left(y-y_{2}\right)^{2}
$$

which can be simplified to $a x+b y=c$, where $a, b, c$ are all rational numbers, and $a, b$ are not both 0. However, from $a \sqrt{2}+b$ $\sqrt{3}=c$ it follows that $a=b=0$.