![\[
\frac{(x+y+z)^5 - x^5 - y^5 - z^5}{(x+y)(y+z)(z+x)} = 0
\]](http://latex.artofproblemsolving.com/7/8/f/78f8e6c2570684631dc288144e13568d71e68ec8.png)
.
and 
.
such that 
are the lengths of a right triangle.
be reals such that 
. Prove that
Let 
. Prove that
.
respectively. 
is the midpoint of arc 
,
is symmetric to 
.
be the incenter and tangent of angles 
respectively. Prove that 
have a common point
and 
.
Y by Adventure10
The sides 
, and 
of a triangle 
are tangent to a circle at points 
respectively. Show that the center of such a circle is on the line that passes through the midpoints of 
and 
.
, and 
of a triangle 
are tangent to a circle at points 
respectively. Show that the center of such a circle is on the line that passes through the midpoints of 
and 
.This post has been edited 1 time. Last edited by parmenides51, May 31, 2019, 9:27 PM
Reason: source edit
Reason: source edit
