Question 116
Let $ABC$ be a triangle such that $AB \lt AC$. Let $D$ be a point on the segment $BC$ such that $BD \lt CD$. The angle bisectors of $\angle ADB$ and $\angle ADC$ meet the segments $AB$ and $AC$ at $E$ and $F$ respectively. Let $\omega$ be the circumcircle of $\triangle AEF$ and $M$ be the midpoint of $EF$. The ray $AD$ meets $\omega$ at $X$ and the line through $X$ parallel to $EF$ meets $\omega$ again at $Y$. If $YM$ meets $\omega$ at $T$, prove that $AT, EF$ and $BC$ are concurrent.