Question 2
Let $BC$ be a diameter of circle $\omega$ with center $O$. Let $A$ be a point of circle $\omega$ such that $0^\circ \lt \angle AOB \lt 120^\circ$. Let $D$ be the midpoint of arc $AB$ not containing $C$. Line $\ell$ passes through $O$ and is parallel to line $AD$. Line $\ell$ intersects line $AC$ at $J$. The perpendicular bisector of segment $OA$ intersects circle $\omega$ at $E$ and $F$. Prove that $J$ is the incenter of triangle $CEF$.