ISL 2006 G10
To each side of a convex polygon we assign the maximum area of a triangle contained in the polygon and having as one of its sides. Show that the sum of the areas assigned to all sides of the polygon is not less than twice the area of the polygon. (Serbia)
Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.
Official text: IMO 2006 Shortlist booklet, page 52.
Solutions
Official solution Solution 1 by the IMO Problem Selection Committee
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