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?
First thought: the ratios should not be dependent on the side lengths because the units are different. So if the the sum of the ratios can be given in terms of a, b, c it is probably a constant.
So I constructed the figure using geometers sketchpad and indeed the sum appears to be a constant 2.

Posted by Jer
on 20110825 13:58:29 