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 November 28th, 2010, 01:28 AM #1 Member   Joined: Oct 2010 Posts: 43 Thanks: 0 R Let $ABC$ be a triangle with incenter $I$ and centroid $G$. Let $R_1,R_2,R_3$ be the circumradili of the triangles $IBC,\ ICA$ and $IAB$ respectively . Let $R'_1,R'_2,R'_3$ be the circumradili of the triangles $GBC,GCA$ and $GAB$ respectively. Prove that $R'_1+R'_2+R'_3 \geq 3R \geq R_1+R_2+R_3.$

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