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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) $ABC$"? – Quintofron Sep 22 '12 at 13:47
Let M,N,P is Midpoint of BC,AC,AB. G is intersection of AM,BN and CP. Sorry because of my bad English – LevanDokite Sep 23 '12 at 6:02
G is the centroid( – lab bhattacharjee Sep 23 '12 at 6:09

I suppose the home work is finished and this answer is for reference.

the answer

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