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
Inside the convex quadrilateral 
, point 
is chosen so that the radii of the circles circumscribed about the triangles 
and 
are equal. For which quadrangles does such a point exist?
, point 
is chosen so that the radii of the circles circumscribed about the triangles 
and 
are equal. For which quadrangles does such a point exist?
