Problem

Source: Moldova TST 2021

Tags: geometry, circumcircle



Acute triangle ABC with AB>BC is inscribed in circle Ω. Points D and E, that lie on (BC) and (AB) are the feet of altitudes from A and C in triangle ABC, and M is the midpoint of the segment DE. Half-line (AM intersects the circle Ω for the second time in N. Show that the circumcenter of triangle MDN lies on the line BC.