CMO 2018 Problem 4

$ABCD$ is a cyclic quadrilateral whose diagonals intersect at $P$ . The circumcircle of $\triangle APD$ meets segment $AB$ at points $A$ and $E$ . The circumcircle of $\triangle BPC$ meets segment $AB$ at points $B$ and $F$ . Let $I$ and $J$ be the incenters of $\triangle ADE$ and $\triangle BCF$ , respectively. Segments $IJ$ and $AC$ meet at $K$ . Prove that the points $A,I,K,E$ are cyclic.