Prove that the line segment, joining the orthocenter and the intersection point of the medians of the acute-angled triangle $ABC$ is parallel to the side $AB$ iff $\tan \angle A \cdot \tan \angle B = 3$.
Problem
Source: 1999 Estonia National Olympiad Final Round grade 12 p3
Tags: Euler Line, Centroid, orthocenter, parallel, geometry, trigonometry