14. Three equally spaced parallel lines intersect a circle, resulting in three chords of lengths $38, 38, 34$. Then the distance between two adjacent parallel chords is ( ).
(A) $5 \frac{1}{2}$
(B) 6
(C) $6 \frac{1}{2}$
(D) 7
(E) $7 \frac{1}{2}$
14. B.

As shown in Figure 11, since the two chords are of equal length, the two chords are on opposite sides of the circle center $O$, and the distance from point $O$ to the two chords is equal, denoted as $d$. Therefore, the distance between the two parallel chords is $2d$.

Let the radius of $\odot O$ be $r$, then $\left\{\begin{array}{l}d^{2}+19^{2}=r^{2}, \\ (3 d)^{2}+17^{2}=r^{2}\end{array} \Rightarrow d=3\right.$. Hence $2 d=6$.