(use in a problem for junior) to practice. Can anyone share to me?
be an odd integer, 
.
integers 
such that for any 
,
and 
.
for which satisfy 
for some 
,
is greater than 
.
such that![\[f(x+yf(x))+f(xf(y)-y)=f(x)-f(y)+2xy\]](http://latex.artofproblemsolving.com/e/b/c/ebccae7e765d9fc3c8605e58a7399a70127b39b1.png)
, such that 
Prove that :
equality cases : ?
Y by Instance, centslordm
Let 
be an acute triangle and let 
and 
be points on the segments 
and 
such that 
. If 
and 
are centers of inscribed circles in triangles 
and 
, and 
is the second intersection point of the circumcircles of and , show that:
Proposed by Nikola Velov
be an acute triangle and let 
and 
be points on the segments 
and 
such that 
. If 
and 
are centers of inscribed circles in triangles 
and 
, and 
is the second intersection point of the circumcircles of and , show that:
Proposed by Nikola Velov
This post has been edited 2 times. Last edited by steppewolf, Apr 30, 2022, 4:08 PM
and 
denote the circumradius of 
and 
,
.
.
,
angle bisector (i.e line 
)
.
and 
.
,
