IMO 1969 LL YUG71

Let four points Ai (i = 1, 2, 3, 4) in the plane determine four

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IMO 1969 LL YUG71

Origin: YUG

Problem

Let four points Ai (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 Ai if S = 180◦?