lies inside triangle 
such that 
and 
.
is the midpoint of segment 
.
lies on segment 
with 
.
.
:![\[
1 \cdot 3 \cdot 5 \cdot \ldots \cdot (2n + 1) \mid (4n + 3)(4n + 5) \cdot \ldots \cdot (8n + 3).
\]](http://latex.artofproblemsolving.com/3/1/a/31a0eac3c7ca298c8fa221083dc94e127e705784.png)
the number of positive integer 
satisfying 
is less than or equal to 
where 
is a constant independent of 
Y by jhu08, centslordm, Honestcobra
Let 
and 
be two positive real numbers, and 
a segment of length on a plane. Let 
be two variable points on the plane such that 
is a non-degenerate convex quadrilateral with 
and 
. It is easy to see that there is a circle tangent to all four sides of the quadrilateral .
Find the precise locus of the point
.
and 
be two positive real numbers, and 
a segment of length on a plane. Let 
be two variable points on the plane such that 
is a non-degenerate convex quadrilateral with 
and 
. It is easy to see that there is a circle tangent to all four sides of the quadrilateral .Find the precise locus of the point
.
,
,
.
lies on a fixed circle of radius 
,
and factor 
(which in fact passws trough 
and let Homothety with center 
.
and 
tangent to 
,
of 
,
,
on it. As the locus of 
,
,
,
