be a monic polynomial with integer coefficient. And suppose there exist 4 distinct integer 
such that 
.
such that 
such that ![\[f(2x+y) + f(x+f(2y)) = f(x)f(y) - xy\]](http://latex.artofproblemsolving.com/0/6/2/0623b7c328af6d088cfc5dd288afe3e17a94ff29.png)
for all reals 
and 
.
sastifying 
Y by
The acute triangle 
has a center at the point 
. A line perpendicular to the line 
at the point intersects the sides 
and 
at the points 
and 
, respectively. The points 
and 
are the incenters of 
and 
. Prove that if the points 
are cyclic, then 
.
has a center at the point 
. A line perpendicular to the line 
at the point intersects the sides 
and 
at the points 
and 
, respectively. The points 
and 
are the incenters of 
and 
. Prove that if the points 
are cyclic, then 
.This post has been edited 1 time. Last edited by parmenides51, Jul 16, 2021, 10:03 AM
