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prove line joining vertices of T_1 and H are perpendicular to sidelines of T_2

Source: Sharygin Finals 2023 9.7

August 2, 2023
geometrySharygin Geometry OlympiadSharygin 2023perpendicular lines

Problem Statement

Let HH be the orthocenter of triangle T\mathrm T. The sidelines of triangle T1\mathrm T_1 pass through the midpoints of T\mathrm T and are perpendicular to the corresponding bisectors of T\mathrm T. The vertices of triangle T2\mathrm T_2 bisect the bisectors of T\mathrm T. Prove that the lines joining HH with the vertices of T1\mathrm T_1 are perpendicular to the sidelines of T2\mathrm T_2.
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