Let ABC be an acute triangle such that AB<AC. Let ω be the circumcircle of ABC
and assume that the tangent to ω at A intersects the line BC at D. Let Ω be the circle with
center D and radius AD. Denote by E the second intersection point of ω and Ω. Let M be the
midpoint of BC. If the line BE meets Ω again at X, and the line CX meets Ω for the second
time at Y, show that A,Y, and M are collinear.Proposed by Nikola Velov, North Macedonia Balkanshortlist2021geometrycollinearityBMO