IMO Shortlist 1969 problem 71
Dodao/la:
arhiva2. travnja 2012. ![(YUG 3)](/media/m/f/5/9/f597d67eea13551b96be03cf4ba66c44.png)
Let four points
![A_i (i = 1, 2, 3, 4)](/media/m/1/3/b/13b84d09b051f010f426161be4818064.png)
in the plane determine four triangles. In each of these triangles we choose the smallest angle. The sum of these angles is denoted by
![S.](/media/m/3/7/7/3772accbdc4fffed2efa17d53f141907.png)
What is the exact placement of the points
![A_i](/media/m/5/f/0/5f0935569a883b13bb70b83ea33eee14.png)
if
![S = 180^{\circ}](/media/m/3/d/b/3db6b4a4470156ed987fa42860f9be99.png)
?
%V0
$(YUG 3)$ Let four points $A_i (i = 1, 2, 3, 4)$ in the plane determine four triangles. In each of these triangles we choose the smallest angle. The sum of these angles is denoted by $S.$ What is the exact placement of the points $A_i$ if $S = 180^{\circ}$?
Izvor: Međunarodna matematička olimpijada, shortlist 1969