Circumcircle x Bisector

Let $ABC$ be an acute, scalene triangle with $AB = 7$, $AC = 10$ and $BC = 8$. The bisector of $\angle BAC$ meets $BC$ at $K$. Let $H$ be the orthocenter of triangle $ABC$, and let line $BH$ meet $AK$ at $E$. The circumcircle of triangle $KBE$ meets line $AB$ again at a point $G \neq B$. Find the length $AG$.