Question 130
Non-equilateral triangle $ABC$ has a $60°$ angle at vertex $A$. Let the angle bisector drawn from vertex $A$ intersect the opposite side at point $D$, and let $Q$ and $R$ be the feet of the altitudes drawn from vertices $B$ and $C$, respectively. Prove that lines $AD$, $BQ$ and $CR$ intersect in three distinct points that are vertices of an equilateral triangle.