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orthocenter of ABC is circumcenter of APQ

Source: 2024 Austrian Regional Competition For Advanced Students p2

March 26, 2024
geometrycircumcircle

Problem Statement

Let ABCABC be an acute triangle with orthocenter HH. The circumcircle of the triangle BHCBHC intersects ACAC a second time in point PP and ABAB a second time in point QQ. Prove that HH is the circumcenter of the triangle APQAPQ.
(Karl Czakler)
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