Question 92
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.