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Problems(1)

Position of points to get sum of minimum to be 180 degrees

Source:

10/4/2010
(YUG3)(YUG 3) Let four points Ai(i=1,2,3,4)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.S. What is the exact placement of the points AiA_i if S=180∘S = 180^{\circ}?
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