Question 97
Let $ABC$ be a triangle with $AB < AC$. Let $\omega$ be a circle passing through $B, C$ and assume that $A$ is inside $\omega$. Suppose $X, Y$ lie on $\omega$ such that $\angle BXA = \angle AYC$ and $X$ lies on the opposite side of $AB$ to $C$ while $Y$ lies on the opposite side of $AC$ to $B$.
Show that, as $X, Y$ vary on $\omega$, the line $XY$ passes through a fixed point.
**Proposed by United Kingdom**
Show that, as $X, Y$ vary on $\omega$, the line $XY$ passes through a fixed point.
**Proposed by United Kingdom**