Question 97
Let $\omega$ be the circumcircle of triangle $ABC$, whose $A$-excenter is $I_A$. Let $D$ be the foot of the perpendicular from $I_A$ to $BC$. Let $M$ be the midpoint of segment $I_A D$. Point $T$ be on arc $BC$ not containing $A$ of $\omega$ satisfying $\angle BAT = \angle DAC$, and $I_A T$ intersects $\omega$ again at $S \neq T$. Let $SM$ and $BC$ intersect at $X$, and let the perpendicular bisector of $AD$ intersect $AC, AB$ at $Y, Z$, respectively. Prove that the lines $AX, BY, CZ$ are concurrent.