,
,
is __
prove that![$\frac{a}{b} + \sqrt {\frac{b}{c}} + \sqrt[3]{{\frac{c}{a}}} > \frac{5}{2}$](http://latex.artofproblemsolving.com/6/a/6/6a657cb647e279b0745e3189c3f9d54aa25bf976.png)
satisfying 
is inscribed in circle 
.
denote its incenter and 
its 
-
denote the midpoint of arc 
.
meets 
.
at 
and 
at 
and 
respectively. The circumcircle of 
meets 
a second time at 
,
meets 
a second time at 
.
passes through the antipodal to 
Y by Adventure10, Mango247
A quadrilateral 
is such that 
and 
. Let 
and 
be the centers of the incircles of triangles 
and 
respectively. Find the angle between the lines 
and 
.
is such that 
and 
. Let 
and 
be the centers of the incircles of triangles 
and 
respectively. Find the angle between the lines 
and 
.
,
