,
,
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 
meets 
a second time at 
,
meets 
a second time at 
.
passes through the antipodal to 
Y by Mango247, Mango247
In a triangle 
with 
, let 
be the projection of 
on 
. Also let 
and 
be the midpoint of the segments 
and respectively and let 
be the projection of 
on 
. Show that the line 
is the tangent at point to the circumscribed circle of the triangle 
.
with 
, let 
be the projection of 
on 
. Also let 
and 
be the midpoint of the segments 
and respectively and let 
be the projection of 
on 
. Show that the line 
is the tangent at point to the circumscribed circle of the triangle 
.
