Question 81
Let $ABC$ be a triangle with $AB = 4$, $BC = 8$, and $CA = 5$. Let $M$ be the midpoint of $BC$, and let $D$ be the point on the circumcircle of $ABC$ so that segment $AD$ intersects the interior of $ABC$, and $\angle BAD = \angle CAM$. Let $AD$ intersect side $BC$ at $X$. Compute the ratio $AX / AD$.