KöMaL 2018 C1484

The diagonals of a convex quadrilateral $ABCD$ are not perpendicular. The feet of the perpendiculars dropped from vertices $A$, $B$, $C$, $D$ onto the sections $AC$ and $BD$ are $A_1$, $B_1$, $C_1$, $D_1$, respectively. (They are different from vertices.) Prove that these points form a quadrilateral similar to the original one.