,
,
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 a triangle with incircle 
and let 
be points outside . Tangents from 
to intersect 
at 
and 
. Points 
and 
are dened similarly. Prove that 
lie on a conic if and only if triangle and 
are perspective.
by Luis Gonzalez, Maracaibo, Venezuela
be a triangle with incircle 
and let 
be points outside . Tangents from 
to intersect 
at 
and 
. Points 
and 
are dened similarly. Prove that 
lie on a conic if and only if triangle and 
are perspective.by Luis Gonzalez, Maracaibo, Venezuela
This post has been edited 1 time. Last edited by parmenides51, Jun 5, 2020, 10:30 PM
Reason: latex
Reason: latex
