Let $\Omega$ and $\omega$ be circles with radii $123$ and $61$, respectively, such that the center of $\Omega$ lies on $\omega$. A chord of $\Omega$ is cut by $\omega$ into three segments, whose lengths are in the ratio $1 : 2 : 3$ in that order. Given that this chord is not a diameter of $\Omega$, compute the length of this chord.

Let's think step by step and output the final answer within \boxed{}.
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