Three concentric circles have radii $1,2,3$. An equilateral triangle with side length $s$ has one vertex on each circle. What is $s^2?$ $\textbf{(A) } 6 \qquad$ $\textbf{(B) } \frac{25}{4} \qquad$ $\textbf{(C) } \frac{13}{2} \qquad$ $\textbf{(D) } \frac{27}{4} \qquad$ $\textbf{(E) } 7$