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Polygon with a center of symmetry

Source: Problem 3, Polish NO 1988

October 16, 2005

symmetrygeometryparallelogramgeometry unsolved

Problem Statement

W

is a polygon which has a center of symmetry

S

such that if

P

belongs to

W

, then so does

P'

, where

S

is the midpoint of

PP'

. Show that there is a parallelogram

V

containing

W

such that the midpoint of each side of

V

lies on the border of

W

.

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