Question 154
Let $ABC$ be an acute triangle. Denote by $O$ the center of its circumcircle. Consider the circle $\Gamma_{B}$ passing through $A$ and $B$ and tangent to $(AC)$, and the circle $\Gamma_{C}$ passing through $A$ and $C$ and tangent to $(AB)$. A line $\Delta$ through $A$ meets $\Gamma_{B}$ again at $X$ and $\Gamma_{C}$ again at $Y$. Show that $OX = OY$.