IMO Shortlist 1985 problem 22


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 6,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
A circle with center O passes through the vertices A and C of the triangle ABC and intersects the segments AB and BC again at distinct points K and N respectively. Let M be the point of intersection of the circumcircles of triangles ABC and KBN (apart from B). Prove that \angle OMB=90^{\circ}.
Izvor: Međunarodna matematička olimpijada, shortlist 1985