Cyclic bashing
by math_explorer, Mar 5, 2011, 2:06 AM
![\[ \sum \cos A = \sum \frac{b^2 + c^2 - a^2}{2bc} = \frac{\sum (ab^2 + ac^2 - a^3)}{2abc} \]](http://latex.artofproblemsolving.com/9/6/0/960a5199eb9e9b3d3835ae77b81c9243ef5b66a6.png)
while
![\[ \frac{r}{R} = \frac{rS}{RS} = \frac{(s-a)(s-b)(s-c)}{abc/4} = \frac{\sum_{sym} ab^2 - \sum a^3 - 2abc}{2abc} \]](http://latex.artofproblemsolving.com/4/8/9/4892141d36cf8dd924eb855593df1c6f33a3da4b.png)
hence
![\[ \frac{r + R}{R} = \sum \cos A \]](http://latex.artofproblemsolving.com/1/1/6/116089389839cca8f95871660019d1b513edb049.png)
This post has been edited 2 times. Last edited by math_explorer, Jun 12, 2011, 7:32 AM
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