3. Given real numbers $a, b, c$ satisfy
$$
a^{2}+b^{2}-4 a \leqslant 1, \quad b^{2}+c^{2}-8 b \leqslant-3,
$$

and $c^{2}+a^{2}-12 c \leqslant-26$.
Then the value of $(a+b)^{c}$ is ( ).
(A) 1
(B) 8
(C) 9
(D) 27
3. D.
From the condition, we have
$$
\begin{array}{l}
\left(a^{2}+b^{2}-4 a\right)+\left(b^{2}+c^{2}-8 b\right)+\left(c^{2}+a^{2}-12 c\right) \leqslant-28 \\
\Rightarrow(a-1)^{2}+(b-2)^{2}+(c-3)^{2} \leqslant 0 \\
\Rightarrow a=1, b=2, c=3 \\
\Rightarrow(a+b)^{c}=3^{3}=27 .
\end{array}
$$