IMO Shortlist 1984 problem 8

  Avg: 0,0
  Avg: 0,0
Dodao/la: arhiva
2. travnja 2012.
Given points O and A in the plane. Every point in the plane is colored with one of a finite number of colors. Given a point X in the plane, the circle C(X) has center O and radius OX+{\angle AOX\over OX}, where \angle AOX is measured in radians in the range [0,2\pi). Prove that we can find a point X, not on OA, such that its color appears on the circumference of the circle C(X).
Izvor: Međunarodna matematička olimpijada, shortlist 1984