Question 16
A circle $\omega$ with centre $I$ is inside another circle $\Omega$ with centre $O$. $AB$ is a chord of $\Omega$ which is tangent to $\omega$. Let $C$ be the circumcentre of $\triangle IAB$. Suppose the radii of $\omega$ and $\Omega$ are $18$ and $54$ respectively and $IO=24$. Find $OC$.