satisfy that: 
and natural number 
,
are there such that 
and 
?
and 
.
be real numbers such that 
Prove that
Let 
Prove that
and 
, then we can deduce 
\le 2 $ ?
satisfying 
.![\[
0 \le (x^2 + 1)(y^2 + 1) + 4(x - 1)(y - 1) \le 164.
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be a sequence defined by 
.
if 
.
Y by Adventure10, Mango247
In the quadrilateral 
and 
are the midpoints of the sides 
and 
respectively, and 
is the midpoint of 
. Suppose 
is the point on the line 
such that 
. Prove that 
.
and 
are the midpoints of the sides 
and 
respectively, and 
is the midpoint of 
. Suppose 
is the point on the line 
such that 
. Prove that 
.
be the midpoint of 
be the foot of the perpendicular from 
to 
and 
be the circle centered at 
with radius 
It's well known that 
is a parallelogram (if not, search up Varignon parallelogram), so 
then must also a parallelogram. Since the circumcenter of 
is 
we find that 
is in fact the radical axis of 
and 
which in particular implies that 
as desired. 
is parallelogram
be a point such thar 
is parallelogram, then 
(1)
(2)
so 
