be distinct natural numbers each of which has exactly 
positive integer factors. For instance, 
has exactly 
.
divides any of the 
'
be an integer. Prove that 
can be written as a polynomial with integer coefficients in the variables 
,
and 
.
,
are real numbers such that 
is an integral multiple of 
.
,
for all positive integers 
.
be the orthocenter of an acute-angled triangle 
.
centered at the midpoint of 
and passing through 
and 
.
,
,
and 
.
with real coefficient. It is known that 
and 
.
can't have 
distinct real roots.
Y by Adventure10
Given is a triangle 
. Let the line through 
parallel to the angle bisector of 
meet the angle bisector of 
at 
, and let the line through parallel to the angle bisector of meet the angle bisector of at 
. Prove that if 
is parallel to 
, then 
.
. Let the line through 
parallel to the angle bisector of 
meet the angle bisector of 
at 
, and let the line through parallel to the angle bisector of meet the angle bisector of at 
. Prove that if 
is parallel to 
, then 
.This post has been edited 1 time. Last edited by lifeisgood03, Jan 18, 2018, 10:32 PM
and 
.
we know that 
and 
are isosceles. Therefore, 
and 
so 
as desired.
is cyclic.
is cyclic.
