HMMT 2017 G7

Let $\omega$ and $\Gamma$ by circles such that $\omega$ is internally tangent to $\Gamma$ at a point $P$. Let $A B$ be a chord of $\Gamma$ tangent to $\omega$ at a point $Q$. Let $R \neq P$ be the second intersection of line $P Q$ with $\Gamma$. If the radius of $\Gamma$ is 17 , the radius of $\omega$ is 7 , and $\frac{A Q}{B Q}=3$, find the circumradius of triangle $A Q R$.