satisfying
Prove
:![\[
1 \cdot 3 \cdot 5 \cdot \ldots \cdot (2n + 1) \mid (4n + 3)(4n + 5) \cdot \ldots \cdot (8n + 3).
\]](http://latex.artofproblemsolving.com/3/1/a/31a0eac3c7ca298c8fa221083dc94e127e705784.png)
and 
.
?
lies inside triangle 
such that 
and 
.
is the midpoint of segment 
.
lies on segment 
with 
.
.
Y by Adventure10, Mango247
Consider the acute-angled triangle 
, altitude 
and point 
- intersection of 
with diameter from 
of circumcircle. Let 
be symmetric points of 
with respect to the lines 
and 
respectively. Prove that 
.
, altitude 
and point 
- intersection of 
with diameter from 
of circumcircle. Let 
be symmetric points of 
with respect to the lines 
and 
respectively. Prove that 
.
.
,
and 
we have
.
