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n + 1 points on sides of regular n-gon, min max area

Source: Polish MO second round 1970 p2

August 28, 2024
geometryareasGeometric Inequalities

Problem Statement

On the sides of the regular n n -gon, n+1 n + 1 points are taken dividing the perimeter into equal parts. At what position of the selected points is the area of the convex polygon with these n+1 n + 1 vertices a) the largest, b) the smallest?
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