Question 49
Let $k$ be a circle centred at $O$ and let $X, A, Y$ be three points on $k$ in this order such that the tangent to the circumcircle of triangle $O X A$ through $X$ and the tangent to the circumcircle of $O A Y$ through $Y$ are parallel. Show that $\angle X A Y=120^{\circ}$ if $A$ lies on the minor arc $X Y$.