IMO Shortlist 1969 problem 10


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 0,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
(BUL 4) Let M be the point inside the right-angled triangle ABC (\angle C = 90^{\circ}) such that \angle MAB = \angle MBC = \angle MCA =\phi. Let \Psi be the acute angle between the medians of AC and BC. Prove that \frac{\sin(\phi+\Psi)}{\sin(\phi-\Psi)}= 5.
Izvor: Međunarodna matematička olimpijada, shortlist 1969