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right angle wanted, orthocenter, circumcenter, midpoint, parallel related

Source: 2018 Grand Duchy of Lithuania, Mathematical Contest p3 (Baltic Way TST)

October 3, 2020
geometryright angleCircumcenter

Problem Statement

The altitudes ADAD and BEBE of an acute triangle ABCABC intersect at point HH. Let FF be the intersection of the line ABAB and the line that is parallel to the side BC and goes through the circumcenter of ABCABC. Let MM be the midpoint of the segment AHAH. Prove that ∠CMF=90o\angle CMF = 90^o
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