6. Given that quadrilateral $A B C D$ is a trapezoid, and $A D / /$ $B C, A D < B C$. Also, $\odot O$ is tangent to $A B$, $A D$, and $C D$ at points $E$, $F$, and $G$ respectively, with the center $O$ on $B C$. Then the relationship between $A B +$ $C D$ and $B C$ is ( ).
(A) greater than
(B) equal to
(C) less than
(D) cannot be determined
6. B.

As shown in Figure 2, let the radius of $\odot O$ be $r$. Connect $O E, O F, O G,$ and $O A, O D$. Then $O E \perp A B, O F \perp A D, O G \perp C D$. Therefore,
$$
O E=O F=O G=r, O F
$$

is the height of trapezoid $A B C D$.
$S_{\triangle O A D}+S_{\triangle O C D}$, we get
$$
\frac{1}{2}(A D+B C)_{r}=\frac{1}{2} A B \cdot r+\frac{1}{2} A D \cdot r+\frac{1}{2} C D \cdot r .
$$

Rearranging the above equation, we obtain $A B+C D=B C$.