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Sharp bounds for the ratio

Source: IMO LongList 1988, Poland 1, Problem 58 of ILL

November 3, 2005
ratiogeometrygeometry unsolved

Problem Statement

For a convex polygon PP in the plane let P′P' denote the convex polygon with vertices at the midpoints of the sides of P.P. Given an integer n≥3,n \geq 3, determine sharp bounds for the ratio area P′area P, \frac{\text{area } P'}{\text{area } P}, over all convex nn-gons P.P.
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