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Locus of orthocentre of PQR is the diameter || to AC.

Source: Sharygin CR P8(Grades 8-9)

March 4, 2022
Sharygin Geometry OlympiadSharygin 2022geometry

Problem Statement

Points P,Q,RP,Q,R lie on the sides AB,BC,CAAB,BC,CA of triangle ABCABC in such a way that AP=PR,CQ=QRAP=PR, CQ=QR. Let HH be the orthocenter of triangle PQRPQR, and OO be the circumcenter of triangle ABCABC. Prove that OH∣∣ACOH||AC.
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