Let $I$ be the center of the circle inscribed in triangle $ABC$ which has $\angle A = 60^o$ and the inscribed circle is tangent to the sideBC at point $D$. Choose points X andYon segments $BI$ and $CI$ respectively, such than $DX \perp AB$ and $DY \perp AC$. Choose a point $Z$ such that the triangle $XYZ$ is equilateral and $Z$ and $I$ belong to the same half plane relative to the line $XY$. Prove that $AZ \perp BC$. (Matthew Kurskyi)