(4) In $\triangle A B C$, $D$ is the midpoint of side $B C$. If $\overrightarrow{A D} \cdot \overrightarrow{A C}=0$, then the value of $\tan A+2 \tan C$ is ( ).
(A) $-\frac{\sqrt{3}}{3}$
(B) 0
(C) $\frac{\sqrt{3}}{3}$
(D) 1
(4) Take the midpoint $E$ of $AB$, then $DE \parallel AC, \angle ADE=90^{\circ}, \angle DAE=A-90^{\circ}$, let $AC=b, AD=m$, then
$$
\tan C=\frac{m}{b}, \tan \left(A-90^{\circ}\right)=\frac{b}{2 m},
$$

which means
$$
-\cot A=\frac{b}{2 m},
$$

so
$$
\tan A=-\frac{2 m}{b},
$$

therefore
$$
\tan A+2 \tan C=0 .
$$

Hence, the answer is B.