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

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October 4, 2010

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Problem Statement

(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

S = 180^{\circ}