Question 181
Let $ABC$ be an acute triangle with $AB \gt AC$. 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 $D$.
$$
\angle AXB - \angle ACB = \angle CYA - \angle CBA
$$
holds, the line $XY$ passes through $D$.