MathDB

1

Part of 2018 China Northern MO

Problems(1)

Parallel Lines

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

7/26/2018
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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