Question 75
Let $ABC$ be a triangle inscribed in circle $(O)$ with incenter $I$. The lines $IB$ and $IC$ intersect $(O)$ again at $J$ and $L$. The circumcircle $(\omega)$ of triangle $IBC$ meets $CA$, $AB$ again at $E$, $F$. Prove that $EL$ and $FJ$ intersect on $(\omega)$.