HMMT 2024 G3

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.