perplexus.info :: Geometry : Sum of Ratios

Sum of Ratios (Posted on 2011-08-25)

Cevians AA', BB', and CC' are concurrent at the incenter I of ΔABC.

What is the value of

    |AI|      |BI|      |CI|
   ------- + ------- + -------
    |AA'|     |BB'|     |CC'|

in terms of the side lengths a, b, and c of ΔABC?

Can you prove it?

See The Solution Submitted by Bractals

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