▪ USA USAMO (junior) 2012

Ημέρα 1η

1. Given a triangle , let and be points on segments and , respectively, such that . Let and be distinct points on segment such that lies between and , , and . Prove that are concyclic (in other words, these four points lie on a circle).
Η λύση της άσκησης από τον Νίκο Φραγκάκη (Doloros).

2. Find all integers such that among any positive real numbers with

  , 

there exist three that are the side lengths of an acute triangle. 

3. Let be positive real numbers. Prove that

  .

Ημέρα 2η

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