Question 167
In triangle $A B C$ the circumcircle has radius $R$ and center $O$ and the incircle has radius $r$ and center $I \neq O$. Let $G$ denote the centroid of triangle $A B C$. Prove that $I G \perp B C$ if and only if $A B=A C$ or $A B+A C=3 B C$.