MathDB

9.7

Part of 2023 Sharygin Geometry Olympiad

Problems(1)

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

Source: Sharygin Finals 2023 9.7

8/2/2023
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.
geometrySharygin Geometry OlympiadSharygin 2023perpendicular lines