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Found problems: 1

2023 Sharygin Geometry Olympiad, 9
Tags: geometry , orthocenter , midpoint of altitude
It is known that the reflection of the orthocenter of a triangle $ABC$ about its circumcenter lies on $BC$. Let $A_1$ be the foot of the altitude from $A$. Prove that $A_1$ lies on the circle passing through the midpoints of the altitudes of $ABC$.