Given a triangle . Let , , be the centroid, the incenter and the orthocenter of triangle , respectively. Prove that .
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Given a triangle $ABC$. Let $G$, $I$, $H$ be the centroid, the incenter and the orthocenter of triangle $ABC$, respectively. Prove that $\angle GIH > 90^{\circ}$.
Izvor: Međunarodna matematička olimpijada, shortlist 1990
Školjka 
. Let 
, 
, 
be the centroid, the incenter and the orthocenter of triangle 
.