Problem

Source: Indian Postal Coaching 2008 set 3 p3

Tags: geometry, max, median, angle bisector



Let $ABC$ be a triangle. For any point $X$ on $BC$, let $AX$ meet the circumcircle of $ABC$ in $X'$. Prove or disprove: $XX'$ has maximum length if and only if $AX$ lies between the median and the internal angle bisector from $A$.