3. Let point $A(2,1)$, moving point $B$ on the $x$-axis, and moving point $C$ on the line $y=x$. Then the minimum value of the perimeter of $\triangle A B C$ is $\qquad$ .
3. $\sqrt{10}$.

Let $P(2,-1), Q(1,2)$ be the points symmetric to point $A$ with respect to the $x$-axis and the line $y=x$, respectively. Then the perimeter of $\triangle A B C$ is
$$
P B+B C+C Q \geqslant P Q=\sqrt{10} .
$$