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Bulgaria 4

Source: IMO LongList 1959-1966 Problem 22

September 1, 2004
geometryparallelogramvectorIMO ShortlistIMO Longlist

Problem Statement

Let PP and P′P^{\prime } be two parallelograms with equal area, and let their sidelengths be a,a, bb and a′,a^{\prime }, b′.b^{\prime }. Assume that a′≤a≤b≤b′,a^{\prime }\leq a\leq b\leq b^{\prime }, and moreover, it is possible to place the segment b′b^{\prime } such that it completely lies in the interior of the parallelogram P.P. Show that the parallelogram PP can be partitioned into four polygons such that these four polygons can be composed again to form the parallelogram P′.% P^{\prime }.
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