(3) Let a tangent line of the circle $x^{2}+y^{2}=1$ intersect the $x$-axis and $y$-axis at points $A$ and $B$, respectively. Then the minimum value of $|AB|$ is $\qquad$
(3) 2 Hint: According to symmetry, without loss of generality, assume the tangent point is $P(\cos \theta, \sin \theta), 0<\theta<\frac{\pi}{2}$, then $|P A|=\tan \theta,|P B|=\cot \theta$. Therefore,
$$
|A B|=|P A|+|P B|=\tan \theta+\cot \theta \geqslant 2,
$$

with equality if and only if $\tan \theta=\cot \theta$, i.e., $\theta=\frac{\pi}{4}$. Hence $|A B|_{\text {min }}=2$.