![$P\in\mathbb{Z}[x]$](http://latex.artofproblemsolving.com/f/3/d/f3d763f4197792a2956273485eb1e94700a43044.png)
has degree 
having 
.
is the leading coefficient of 
.
,
be all positive integers smaller than 
such that 
for all 
is the largest positive integer that divides both 
.
.
that satisfy 
are positive real numbers, then
Y by
Given an acute triangle 
we construct exterior triangles 
and 
such that 
and 
. Let 
, 
, 
be the feet of the heights of triangle , and let 
and 
be the midpoints of 
and 
respectively. Show that the circumcenters of the triangles 
, 
and 
are collinear.
we construct exterior triangles 
and 
such that 
and 
. Let 
, 
, 
be the feet of the heights of triangle , and let 
and 
be the midpoints of 
and 
respectively. Show that the circumcenters of the triangles 
, 
and 
are collinear.
