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Nice geometry - paralellogram

Source: JBHMO (JBMO TST Bosnia and Herzegovina, Problem 3)

June 5, 2008
geometryparallelogramtrapezoid

Problem Statement

Point M M is given in the interior of parallelogram ABCD ABCD, and the point N N inside triangle AMD AMD is chosen so that < MNA \plus{} < MCB \equal{} MND \plus{} < MBC \equal{} 180^0. Prove that MN MN is parallel to AB AB.
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