3. Let point $A(2,0)$, point $B$ be on the curve $y=\sqrt{1-x^{2}}$, and $\triangle A B C$ be an isosceles right triangle with $A$ as the right-angle vertex. Then the maximum value of $|O C|$ is $\qquad$.
3. $2 \sqrt{2}+1$.

As shown in Figure 2, the trajectory of point $C$ is a semicircular arc with center $D(2,2)$ (in fact, by rotating $\triangle A O B$ $90^{\circ}$ clockwise around point $A$).
$$
\text { Therefore, } |O C|_{\max }=O D+1=2 \sqrt{2}+1 \text {. }
$$