Question 60
$\triangle ABC$ is an isosceles triangle with $AB = AC$. Point $X$ is an arbitrary point on side $BC$. Points $Y, Z$ are on the sides $AB, AC$, respectively, such that $\angle BXY = \angle ZXC$. A line parallel to $YZ$ and passing through $B$ cuts $XZ$ at $T$. Prove that $AT$ bisects $\angle A$.