IMO Shortlist 1973 problem 14

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Dodao/la: arhiva
April 2, 2012
A soldier needs to check if there are any mines in the interior or on the sides of an equilateral triangle ABC. His detector can detect a mine at a maximum distance equal to half the height of the triangle. The soldier leaves from one of the vertices of the triangle. Which is the minimum distance that he needs to traverse so that at the end of it he is sure that he completed successfully his mission?
Source: Međunarodna matematička olimpijada, shortlist 1973