AHSME 1973 Problem 1

A chord which is the perpendicular bisector of a radius of length 12 in a circle, has length $\textbf{(A)}\ 3\sqrt3 \textbf{(B)}\ 27 \textbf{(C)}\ 6\sqrt3 \textbf{(D)}\ 12\sqrt3 \textbf{(E)}\ \text{ none of these}$