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Parallel Lines

Source: 2018 China North Mathematical Olympiad Grade 10 Test 1 P1

July 26, 2018
geometryChinaParallel Linesincentercircumcircle

Problem Statement

In triangle ABCABC, let the circumcenter, incenter, and orthocenter be OO, II, and HH respectively. Segments AOAO, AIAI, and AHAH intersect the circumcircle of triangle ABCABC at DD, EE, and FF. CDCD intersects AEAE at MM and CECE intersects AFAF at NN. Prove that MNMN is parallel to BCBC.
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