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Geometry Mathley 1.2 orthocenter

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June 6, 2020
orthocentergeometryaltitudes

Problem Statement

Let ABCABC be an acute triangle with its altitudes BE,CFBE,CF. MM is the midpoint of BCBC. NN is the intersection of AMAM and EF.XEF. X is the projection of NN on BCBC. Y,ZY,Z are respectively the projections of XX onto AB,ACAB,AC. Prove that NN is the orthocenter of triangle AYZAYZ.
Nguyễn Minh Hà
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