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<MNA+<MCB=<MND+<MBC=180^o- All-Russian MO 2004 Regional (R4) 9.7

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September 27, 2024
parallelgeometryanglesparallelogram

Problem Statement

Inside the parallelogram ABCDABCD, point MM is chosen, and inside the triangle AMDAMD, point NN is chosen in such a way that ∠MNA+∠MCB=∠MND+∠MBC=180o.\angle MNA + \angle MCB =\angle MND + \angle MBC = 180^o. Prove that lines MNMN and ABAB are parallel.
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