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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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    G is the centroid(http://www.jimloy.com/geometry/centers.htm)2012-09-23

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

the answer