Question 102
Let $ABC$ be an acute triangle with $AB \gt AC$ and intersection point $H$. Let $D$ be the base point of $A$ on $BC$. Let $E$ be the reflection of $C$ on $D$. The lines $AE$ and $BH$ intersect at the point $S$. Let $N$ be the midpoint of $AE$ and let $M$ be the midpoint of $BH$. Prove that $MN$ is perpendicular to $DS$.
Figure 3: Figure for solving task 4
Figure 3: Figure for solving task 4