Advanced Number Theory · Hard problem

A circle $\Omega$ has center $O$ and radius $13$. Two parallel chords of $\Omega$ have lengths $10$ and $24$ and lie on opposite sides of $O$. A circle $\omega$ lies between the two chords, tangent to both of them and internally tangent to $\Omega$. The distance $O$ to the center of $\omega$ is $\dfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.