IMO Shortlist 2002 problem G7

  Avg: 0,0
  Avg: 9,0
The incircle \Omega of the acute-angled triangle ABC is tangent to its side BC at a point K. Let AD be an altitude of triangle ABC, and let M be the midpoint of the segment AD. If N is the common point of the circle \Omega and the line KM (distinct from K), then prove that the incircle \Omega and the circumcircle of triangle BCN are tangent to each other at the point N.
Izvor: Međunarodna matematička olimpijada, shortlist 2002