Question 71
Given is a triangle $ABC$ and a circle $\omega$ with center $I$ that touches $AB$, $AC$ and meets $BC$ at $X$, $Y$. The line through $I$ perpendicular to $BC$ meets the line through $A$ parallel to $BC$ at $Z$. Show that the circumcircles of $\triangle XYZ$ and $\triangle ABC$ are tangent to each other.