satisfy that: 
,![\[
\sqrt{a + b} + \sqrt{b + c} + \sqrt{c + a} \geq \frac{4(ab + bc + ca)}{\sqrt{(a + b)(b + c)(c + a)}}
\]](http://latex.artofproblemsolving.com/e/7/2/e72fd0f134289c359bc8766440babc52ae131961.png)
satisfied 
Find the minimum of 
Y by Mango247
Consider the triangle 
, where 
, and 
is the midpoint of the side ![$[BC]$](//latex.artofproblemsolving.com/e/a/1/ea1d44f3905940ec53e7eebd2aa5e491eb9e3732.png)
. Let point 
be such that ![$[NC] = [AB]$](//latex.artofproblemsolving.com/9/c/b/9cb811644430a117fa3767a6f2aa7e4d73900ad7.png)
. Show that 
is the angle bisector of 
, where 
, and 
is the midpoint of the side ![$[BC]$](http://latex.artofproblemsolving.com/e/a/1/ea1d44f3905940ec53e7eebd2aa5e491eb9e3732.png)
. Let point 
be such that ![$[NC] = [AB]$](http://latex.artofproblemsolving.com/9/c/b/9cb811644430a117fa3767a6f2aa7e4d73900ad7.png)
. Show that 
is the angle bisector of 
