HMMT 2020 G8

Let $A B C$ be an acute triangle with circumcircle $\Gamma$. Let the internal angle bisector of $\angle B A C$ intersect $B C$ and $\Gamma$ at $E$ and $N$, respectively. Let $A^{\prime}$ be the antipode of $A$ on $\Gamma$ and let $V$ be the point where $A A^{\prime}$ intersects $B C$. Given that $E V=6, V A^{\prime}=7$, and $A^{\prime} N=9$, compute the radius of $\Gamma$.