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Prove that lines $MN$ and $AC$ are parallel.

Source: Moldova EGMO TST 2021

February 4, 2023
geometry

Problem Statement

In triangle ABCABC point MM is on side ABAB such that AM:AB=3:4AM:AB=3:4 and point PP is on side BCBC such that CP:CB=3:8CP:CB=3:8. Point NN is symmetric to AA with respect to point PP. Prove that lines MNMN and ACAC are parallel.
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