3. Given real numbers $a, b, c$ satisfy the inequalities
$$
|a| \geqslant|b+c|,|b| \geqslant|c+a|,|c| \geqslant |a+b|
$$

then the value of $a+b+c$ is ( ).
(A) 0
(B) 1
(C) 2
(D) 3
3. A.

From the given conditions, we have
$$
\begin{array}{l}
a^{2} \geqslant(b+c)^{2}=b^{2}+2 b c+c^{2}, \\
b^{2} \geqslant(c+a)^{2}=c^{2}+2 c a+a^{2}, \\
c^{2} \geqslant(a+b)^{2}=a^{2}+2 a b+b^{2} .
\end{array}
$$

Adding the three inequalities, we get
$$
a^{2}+b^{2}+c^{2} \geqslant 2\left(a^{2}+b^{2}+c^{2}\right)+2 a b+2 b c+2 c a \text {. }
$$

Thus, we have $(a+b+c)^{2} \leqslant 0$.
Therefore, $a+b+c=0$.