,![\[
\frac{ab}{b+1} + \frac{bc}{c+1} + \frac{ca}{a+1} \geq \frac{3abc}{1 + abc}
\]](http://latex.artofproblemsolving.com/d/5/8/d582a3269c92041834c02153ee8e946a274e52bd.png)
and 
be positive integers.
and 
.
.
![\[
\frac{a}{b} + \frac{b}{c} + \frac{c}{a}.
\]](http://latex.artofproblemsolving.com/3/2/b/32b41635c159921e11245369e66185ec69b0d785.png)
Y by
In a convex hexagon 
, the internal angles at the vertices 
are equal. Moreover, equality is satisfied
. Show that the line 
and the perpendicular bisectors of segments 
and 
have a point common.
, the internal angles at the vertices 
are equal. Moreover, equality is satisfied
. Show that the line 
and the perpendicular bisectors of segments 
and 
have a point common.This post has been edited 2 times. Last edited by parmenides51, Apr 13, 2021, 3:52 PM
