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3.(Well-known Euler line)let G=centroid H=orthocentre,I=incenter,O=circumcenter
Prove that $H,G,O$ collinear$ ( HG:GO=2:1)$
4.$a,b,c>0$ and $a+b+c\geq \frac{1}{a}+\frac{1}{b}+\frac{1}{c}$ show that
$a+b+c\geq \frac{3}{a+b+c}+\frac{2}{abc}$