Problem #WSP-5297

Problem

Let $ABC$ be a non-isosceles triangle. The point $G$ is the point of intersection of the medians $AE$, $BF$, $CD$, the point $H$ is the point of intersection of all heights, the point $I$ is the center of the circumscribed circle for $ABC$, or the point of intersection of all perpendicular bisectors to the segments $AB$, $BC$, $AC$.
Prove that points $I,G,H$ lie on one line and the ratio $IG:GH=1:2$.