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reflection of K wrt OH lies on BC, orthocenter, 2 circumcenters

Source: 2021 Dutch IMO TST 1.3

December 29, 2021
geometryorthocentercollinearcircumcircle

Problem Statement

Let ABCABC be an acute-angled and non-isosceles triangle with orthocenter HH. Let OO be the center of the circumscribed circle of triangle ABCABC and let KK be center of the circumscribed circle of triangle AHOAHO. Prove that the reflection of KK wrt OHOH lies on BCBC.
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