
Let four points

in the plane determine four triangles. In each of these triangles we choose the smallest angle. The sum of these angles is denoted by

What is the exact placement of the points

if

?
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$(YUG 3)$ 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 $S = 180^{\circ}$?