MEMO 2015 Problem 5

Let $ABC$ be an acute triangle with $AB>AC$ . Prove that there exists a point $D$ with the following property: whenever two distinct points $X$ and $Y$ lie in the interior of $ABC$ such that the points $B$ , $C$ , $X$ , and $Y$ lie on a circle and $$\angle AXB-\angle ACB=\angle CYA-\angle CBA$$ holds, the line $XY$ passes through $D$ .