,![\[
\sqrt{a + b} + \sqrt{b + c} + \sqrt{c + a} \geq \frac{4(ab + bc + ca)}{\sqrt{(a + b)(b + c)(c + a)}}
\]](http://latex.artofproblemsolving.com/e/7/2/e72fd0f134289c359bc8766440babc52ae131961.png)
satisfied 
Find the minimum of 
Y by
In rectangle 
, point 
is the foot of the perpendicular from vertex 
on the diagonal 
, points 
and 
are the midpoints of the segments 
and 
, respectively. Prove that 
is a right angle.
, point 
is the foot of the perpendicular from vertex 
on the diagonal 
, points 
and 
are the midpoints of the segments 
and 
, respectively. Prove that 
is a right angle.
,
.
,
is cyclic, implying 
.
