KöMaL 2023 C1769

The orthocentre of an acute-angled triangle $ABC$ is $M$, and $AB\ge BC \ge CA$ for the sides. The perpendicular bisector of line segment $AM$ intersects side $AC$ at $D$, and the perpendicular bisector of line segment $BM$ intersects side $BC$ at $E$. Find the angles of triangle $ABC$, given that points $D$, $M$, $E$ are collinear.