Question 122
Let $E$ be an ellipse and let's consider three parallel lines $r_{1}, r_{2}$ and $r_{3}$, each of which cuts $E$ at two different points. Be these points $A_{1}, B_{1}, A_{2}, B_{2}$ and $A_{3}, B_{3}$, respectively. Prove that the midpoints of the $A_{1} B_{1}, A_{2} B_{2}$ and $A_{3} B_{3}$ segments are aligned.