Question 2
Let $ABC$ be an acute scalene triangle with orthocenter $H$. Let $D,E,F$ be the reflections of $H$ in $BC,CA,AB$, respectively, and let $A^{\prime},B^{\prime},C^{\prime}$ be the reflections of $A,B,C$ in those same respective lines. Let $S$ be the circumcenter of $A^{\prime} B^{\prime} C^{\prime}$, and $H^{\prime}$ the orthocenter of $DEF$. Let $J$ be the center of the circle through the three perpendicular projections of $H$ onto $B^{\prime} C^{\prime},C^{\prime} A^{\prime},A^{\prime} B^{\prime}$. Prove that $HJ\parallel H^{\prime} S$.