![$P\in\mathbb{Z}[x]$](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 Adventure10
In an acute triangle 
, the feet of the perpendiculars from 
and 
to the opposite sides are 
and 
, respectively. The line passing through and parallel to 
intersects 
at 
, the line passing through and parallel to 
intersects at 
. The feet of the perpendiculars from to 
and 
are 
and 
, respectively. 
intersects 
at 
. Prove that 
.
, the feet of the perpendiculars from 
and 
to the opposite sides are 
and 
, respectively. The line passing through and parallel to 
intersects 
at 
, the line passing through and parallel to 
intersects at 
. The feet of the perpendiculars from to 
and 
are 
and 
, respectively. 
intersects 
at 
. Prove that 
.
as then we will be done from Simson line 
by parallel lines and angle-chasing, so 
cyclic, and we are done 
means 
should be cyclic.Let 
and 
.
,and 
. So 
. If 
we will be done.Notice that 
since 
.
is cyclic, then 
. And since 
, 
