,
,
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
Let 
be the circumcircle of triangle 
, and 
a point on the arc 
not containing 
. 
is the -mixtilinear circle of triangle , and 
are the -mixtilinear circles of triangle 
respectively. Prove that there is a line tangent to all the three circles 
and 
.
Nguyen Van Linh, a student at Hanoi Foreign Trade University Cabinet
be the circumcircle of triangle 
, and 
a point on the arc 
not containing 
. 
is the -mixtilinear circle of triangle , and 
are the -mixtilinear circles of triangle 
respectively. Prove that there is a line tangent to all the three circles 
and 
.Nguyen Van Linh, a student at Hanoi Foreign Trade University Cabinet
This post has been edited 2 times. Last edited by parmenides51, Aug 20, 2020, 8:07 AM
