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
On the small arcs 
, 
of the circumscribed circle of the triangle 
are given the points 
, 
respectively such that 
, where 
is the center of the circle inscribed in the triangle 
. Prove that the lines 
and 
are perpendicular
, 
of the circumscribed circle of the triangle 
are given the points 
, 
respectively such that 
, where 
is the center of the circle inscribed in the triangle 
. Prove that the lines 
and 
are perpendicular
