Question 62
The nine-point circle of scalene $\triangle ABC$ touches with incircle of $\triangle ABC$ at point $S$. $AD$, $BE$ and $CF$ are heights. If reflection of $DS$ over $AD$ is $\ell_1$, reflection of $ES$ over $BE$ is $\ell_2$ and reflection of $FS$ over $CF$ is $\ell_3$, then prove that $\ell_1 \parallel \ell_2 \parallel \ell_3$.