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in a parallelogram, equal segments given and wanted

Source: 2014 Oral Moscow Geometry Olympiad grades 8-9 p2

August 9, 2019
geometryparallelogramequal segments

Problem Statement

Let ABCDABCD be a parallelogram. On side ABAB, point MM is taken so that AD=DMAD = DM. On side ADAD point NN is taken so that AB=BNAB = BN. Prove that CM=CNCM = CN.
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