IMO Shortlist 1973 problem 3
Dodao/la:
arhiva2. travnja 2012. Prove that the sum of an odd number of vectors of length 1, of common origin
![O](/media/m/9/6/0/9601b72f603fa5d15addab9937462949.png)
and all situated in the same semi-plane determined by a straight line which goes through
![O,](/media/m/2/7/9/2793010f44f28029d298a7894a5228fe.png)
is at least 1.
%V0
Prove that the sum of an odd number of vectors of length 1, of common origin $O$ and all situated in the same semi-plane determined by a straight line which goes through $O,$ is at least 1.
Izvor: Međunarodna matematička olimpijada, shortlist 1973