Question 2
Let $A_0,B_0,C_0$ respectively be the midpoints of the altitudes $AH,BK,CL$ of a non-equilateral triangle $ABC$. Let $O$ and $I$ be its circumcenter and incenter. Its incircle touches $BC,CA,AB$ at $D,E,F$, respectively. Prove that $A_0D,B_0E,C_0F,OI$ are concurrent.