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Prove that lines parallel in triangle

Source: Mongolian MO 2007 Grade 11 P1

April 8, 2021
geometry

Problem Statement

Let MM be the midpoint of the side BCBC of triangle ABCABC. The bisector of the exterior angle of point AA intersects the side BCBC in DD. Let the circumcircle of triangle ADMADM intersect the lines ABAB and ACAC in EE and FF respectively. If the midpoint of EFEF is NN, prove that MN∥ADMN\parallel AD.
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