NO-ABEL 2019 Problem 4

The diagonals of a convex quadrilateral $ABCD$ intersect at $E$ . The triangles $ABE, BCE, CDE$ and $DAE$ have centroids $K,L,M$ and $N$ , and orthocentres $Q,R,S$ and $T$ . Show that the quadrilaterals $QRST$ and $LMNK$ are similar.