TSTST 2013 Problem 4

Circle $\omega$, centered at $X$, is internally tangent to circle $\Omega$, centered at $Y$, at $T$. Let $P$ and $S$ be variable points on $\Omega$ and $\omega$, respectively, such that line $P S$ is tangent to $\omega($ at $S)$. Determine the locus of $O$ - the circumcenter of triangle $P S T$.