IMO Shortlist 1993 problem G3


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 7,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
Let triangle ABC be such that its circumradius is R = 1. Let r be the inradius of ABC and let p be the inradius of the orthic triangle A'B'C' of triangle ABC. Prove that p \leq 1 - \frac{1}{3 \cdot (1+r)^2}.
Izvor: Međunarodna matematička olimpijada, shortlist 1993