Question 5
Triangle $ABC$ has centroid $G$ and is inscribed in a circle of radius $R$. The medians from $A,B,C$, extended, meet the circle again at $D,E,F$, respectively. Prove that
$$\frac3R\le\frac1{GD}+\frac1{GE}+\frac1{GF}\le\sqrt3\left(\frac1{AB}+\frac1{BC}+\frac1{CA}\right).$$
$$\frac3R\le\frac1{GD}+\frac1{GE}+\frac1{GF}\le\sqrt3\left(\frac1{AB}+\frac1{BC}+\frac1{CA}\right).$$