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Well-known orthocenter problem

Source: Austria MO Final round 2023 P5

May 27, 2023
geometry

Problem Statement

Let ABCABC be an acute triangle with AC≠BCAC\neq BC, MM the midpoint of side ABAB, HH is the orthocenter of △ABC\triangle ABC, DD on BCBC is the foot of the altitude from AA and EE on ACAC is the foot of the perpendicular from BB. Prove that the lines AB,DEAB, DE and the perpendicular to MHMH through CC are concurrent.
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