6. As shown in Figure $1, A B, C D$, and $P Q$ are three chords of $\odot O$, $A B \perp P Q, C D \perp P Q$, $M, N$ are the feet of the perpendiculars. If $A B \leqslant$ $C D$, then we have $($.
(A) $\frac{A M}{B M} \geqslant \frac{C N}{D N}$
(B) $\frac{A M}{E M} \leqslant \frac{C}{D N}$
(C) $\frac{A M}{B M} \neq \frac{C N}{D N}$
(D) Cannot determine the relationship between $\frac{A M}{B M}$ and $\frac{C N}{D N}$
6. (A).

As shown in Figure 6, let $A B=$
$$
\begin{array}{l}
2 a, C D=2 b, \text { obviously } \\
a \leqslant b . \\
\text { Let } O S=x, \text { then } X M \\
=Y N=O S=x . \text { Therefore, } \\
\frac{A M}{M B}-\frac{C N}{D N} \\
=\frac{a+x}{a-x}-\frac{b+x}{b-x} \\
=\frac{1}{(a-x)(b-x)}[(a+x)(b-x)-(b+x) \cdot \\
=\frac{(a-x)]}{(a-x)(b-x)} \cdot 2 x \cdot(b-a) \geqslant 0 .
\end{array}
$$