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MathNet 2009-part-03 — 175 problems (EN–VI) Question 158

Math Olympiad Vault · MathNet 2009-part-03 — 175 problems (EN–VI)

Question 158

Let $ABC$ be an acute non-isosceles triangle. Let $AA'$, $H$, $O$ be its altitude, orthocenter, and circumcenter respectively. Prove that the point symmetrical to the circumcenter of triangle $HOA'$ about line $HO$ lies on a midline of triangle $ABC$. (D. Prokopenko)