Question 3
Let $ABC$ be an acute scalene triangle. Its incircle touches $BC,CA,AB$ at $D,E,F$, respectively. Let $X,Y,Z$ be the feet of the altitudes from $A,B,C$, respectively. Let $A'$ be the reflection of $X$ across $EF$, let $B'$ be the reflection of $Y$ across $FD$, and let $C'$ be the reflection of $Z$ across $DE$. Prove that triangles $ABC$ and $A'B'C'$ are similar.