IMO 1984 LL SPA54

Let P be a convex planar polygon with equal angles. Let

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IMO 1984 LL SPA54

Origin: SPA

Problem

Let P be a convex planar polygon with equal angles. Let l1, . . . , ln be its sides. Show that a necessary and sufficient condition for P to be regular is that the sum of the ratios li li+1 (i = 1, . . . , n; ln+1 = l1) equals the number of sides.