Question 2
Let $ABC$ be a triangle with $AC \gt AB$. Let a circle $\omega$ tangent to the sides $AB$ and $AC$ at $D$ and $E$ respectively, intersects the circumcircle of $ABC$ at $K$ and $L$ and $X$ and $Y$ be points on the sides $AB$ and $AC$ respectively, such that
$$
\frac{AX}{AB} = \frac{CE}{BD + CE} \quad \text{and} \quad \frac{AY}{AC} = \frac{BD}{BD + CE}.
$$
Show that the lines $XY$, $BC$ and $KL$ are concurrent.
$$
\frac{AX}{AB} = \frac{CE}{BD + CE} \quad \text{and} \quad \frac{AY}{AC} = \frac{BD}{BD + CE}.
$$
Show that the lines $XY$, $BC$ and $KL$ are concurrent.