Question 14
Let $ABCD$ be a cyclic quadrilateral and $\omega$ its circumcircle. Let $I$, $J$, and $K$ be the incenters of the triangles $ABC$, $ACD$, and $ABD$, respectively. Also, let $E$ be the midpoint of the arc $DB$ of $\omega$ containing $A$. The line $EK$ intersects $\omega$ at $F$ ($F \neq E$). Prove that the points $C$, $F$, $I$, and $J$ lie on the same circle.