IMO Shortlist 1966 problem 41
Dodao/la:
arhiva2. travnja 2012. Given a regular
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
-gon
![A_{1}A_{2}...A_{n}](/media/m/f/4/8/f481ae2ac668ca31083c16c6cc54cae3.png)
(with
![n\geq 3](/media/m/d/f/e/dfe037b8debb8aa67d6ed7ad5e28cc6c.png)
) in a plane. How many triangles of the kind
![A_{i}A_{j}A_{k}](/media/m/c/4/2/c42858dc448135f5dfb2570a6eb987ac.png)
are obtuse ?
%V0
Given a regular $n$-gon $A_{1}A_{2}...A_{n}$ (with $n\geq 3$) in a plane. How many triangles of the kind $A_{i}A_{j}A_{k}$ are obtuse ?
Izvor: Međunarodna matematička olimpijada, shortlist 1966