Question 140
Let the line $l_0$ be tangent to the circumcircle of a scalene triangle $ABC$ at the point $A$. A variable line $l$ parallel to $l_0$ intersects the sides $AB$ and $AC$ at points $X$ and $Y$, respectively. Let $T$ be the point of intersection of $BY$ and $CX$. Let $Z$ be the second intersection point of the line $AT$ and the circumcircle of $ABC$. Show that as $l$ changes, the circumcircles of all triangles $XYZ$ pass through some fixed point.