2021 AMC 10B Problem 14

Three equally spaced parallel lines intersect a circle, creating three chords of lengths 38, 38, and 34. What is the distance between two adjacent parallel lines?

\textbf{(A)} ~5\frac{1}{2} \qquad\textbf{(B)} ~6 \qquad\textbf{(C)} ~6\frac{1}{2} \qquad\textbf{(D)} ~7 \qquad\textbf{(E)} ~7\frac{1}{2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.