IMO 1988 LL POL69

For a convex polygon P in the plane let P ′ denote the convex

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IMO 1988 LL POL69

Origin: POL

Problem

For a convex polygon P in the plane let P ′ denote the convex polygon with vertices at the midpoints of the sides of P. Given an integer n \geq3, determine sharp bounds for the ratio area(P ′) area(P) over all convex n-gons P.