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Geometry Problem 765: Triangle, Inradius, Exradii, Three Exradius, Harmonic Mean. Level: High School, College.

The figure shows a triangle ABC with the inradius r and the exradii ra, rb, rc. Prove that the inradius is one-third the harmonic mean of the exradii, therefore, Formula to prove.
 

Triangle, Inradius, Exradii, Harmonic Mean
 


 

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