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Let triangle $ABC, BC=a,AB=c,AC=b$. Know that the bisector of $ACB$ perpendicular with the line $OG$, with $O$ is inscribed circle center and $G$ is center of $ABC$. Prove that: $$\frac{2ab}{a+b}=\frac{a+b+c}{3}$$

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    What do you mean by "$G$ being the center of (triangle) $ABC$"?2012-09-22
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    Let M,N,P is Midpoint of BC,AC,AB. G is intersection of AM,BN and CP. Sorry because of my bad English2012-09-23
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    G is the centroid(http://www.jimloy.com/geometry/centers.htm)2012-09-23

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