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orthocentral bisection

Source: Sharygin Final 2024 8.2

August 2, 2024
geometrySharygin Geometry OlympiadSharygin 2024

Problem Statement

Let CMCM be the median of an acute-angled triangle ABCABC, and PP be the projection of the orthocenter HH to the bisector of ∠C\angle C. Prove that MPMP bisects the segment CHCH.
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