Question 8
In acute triangle $ABC$, points $D, E, F$ are the altitude feet from $A, B, C$ respectively. Let $I_1, I_2$ be the incenters of $AEF$ and $BDF$, and $O_1, O_2$ the circumcenters of $ACI_1$ and $BCI_2$ respectively. Prove lines $I_1I_2$ and $O_1O_2$ parallel.