Question 65
Let $D$ be the point on the arc $AC$ of the circumcircle of the triangle $ABC$ ($AB \lt BC$), that doesn't contain point $B$. Let $X$ and $X'$ be any two points on the side $AC$ such that $\angle ABX = \angle CBX'$. Show that regardless of the choice of point $X$, the circumcircle of $\triangle DXX'$ passes through a fixed point different from $D$.