IOM 2020 Problem 6

In convex pentagon $ABCDE$ points $A_1$ , $B_1$ , $C_1$ , $D_1$ , $E_1$ are intersections of pairs of diagonals $(BD, CE)$ , $(CE, DA)$ , $(DA, EB)$ , $(EB, AC)$ and $(AC, BD)$ respectively. Prove that if four of quadrilaterals $AB_{1}A_{1}B$ , $BC_{1}B_{1}C$ , $CD_{1}C_{1}D$ , $DE_{1}D_{1}E$ and $EA_{1}E_{1}A$ are cyclic then the fifth one is also cyclic.