Problem

Source: All-Russian MO 2009 Regional 11. 4

Tags: geometry, midline



In an acute non-isosceles triangle $ABC$, the altitude $AA'$ is drawn and point $H$ is the intersection point of the altitudes and and $O$ is the center of the circumscribed circle. Prove that the point symmetric to the circumcenter of triangle $HOA'$ wrt straight line $HO$, lies on a midline of triangle $ABC$.