6. If $a, b, c$ and $t_{a}, t_{b}, t_{c}$ represent the lengths of the three sides and the three angle bisectors of $\triangle ABC$, respectively, then among the following conclusions:
(1) $t_{a} t_{b} t_{c}>a b c$,
(2) $t_{a} t_{b} t_{c}=\sqrt{a b c}$,
(3) $t_{a} t_{b} t_{c}<a b c$,
(4) $t_{a} t_{b} t_{c}=a b c$, the correct one(s) is/are ( ).
(A)(2)
(B)(1)(4)
(C)(3)(4)
(D)(3)
6.D.

As shown in Figure 6, construct the circumcircle $\odot O$ of $\triangle ABC$, and let $AD$ be the angle bisector of $\angle BAC$. Extend $AD$ to intersect $\odot O$ at point $E$, and connect $BE$ and $CE$.
From $\triangle ABD \sim \triangle AEC$, we get $bc = t_a AE$.
Let $AE = x$, i.e., $bc = t_a x$.
Similarly, let the extensions of the angle bisectors of $\angle B$ and $\angle C$ intersect $\odot O$ at segments $y$ and $z$, respectively. Therefore,
$$
\begin{aligned}
ba & = t_b y, ab = t_c z \\
\text{Also, } x & > t_a, y > t_b, z > t_c, \text{ then } \\
(a b c)^2 & = t_a t_b t_c \cdot x y z > (t_a t_b t_c)^2
\end{aligned}
$$