Let ABCD be a convex quadrilateral. Points X and Y lie on the extensions beyond D of the sides CD and AD respectively in such a way that DX=AB and DY=BC. Similarly points Z and T lie on the extensions beyond B of the sides CB and AB respectively in such a way that BZ=AD and BT=DC. Let M1 be the midpoint of XY, and M2 be the midpoint of ZT. Prove that the lines DM1,BM2 and AC concur. geometryconcurrencySharygin Geometry OlympiadSharygin 2023