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is it true that ABCD is parallelogram ?

Source: 2017 Oral Moscow Geometry Olympiad grades 8-9 p3

July 26, 2019
geometryparallelogrammidpoints

Problem Statement

Points MM and NN are the midpoints of sides ABAB and CDCD, respectively of quadrilateral ABCDABCD. It is known that BC//ADBC // AD and AN=CMAN = CM. Is it true that ABCDABCD is parallelogram?
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