Let $O$ be the circumcenter of triangle $ABC$ with $|AB|=5$, $|BC|=6$, $|AC|=7$. Let $A_1$, $B_1$, $C_1$ be the reflections of $O$ over the lines $BC$, $AC$, $AB$, respectively. What is the distance between $A$ and the circumcenter of triangle $A_1B_1C_1$?

$ 
\textbf{(A)}\ 6
\qquad\textbf{(B)}\ \sqrt {29}
\qquad\textbf{(C)}\ \dfrac {19}{2\sqrt 6}
\qquad\textbf{(D)}\ \dfrac {35}{4\sqrt 6}
\qquad\textbf{(E)}\ \sqrt {\dfrac {35}3}
$