[/quote]
,
be positive real numbers so that 
.![\[ \left( a - 1 + \frac 1b \right) \left( b - 1 + \frac 1c \right) \left( c - 1 + \frac 1a \right) \leq 1.
\]](http://latex.artofproblemsolving.com/7/6/e/76e794a62090c8c4b5f3a70ad4d036669418ca69.png)
,
,
cut three common chords concurrent at 
.
,
which are internally tangent to all 
.
and 
be positive real numbers such that 
.![\[
\frac{x^{3}}{(1 + y)(1 + z)}+\frac{y^{3}}{(1 + z)(1 + x)}+\frac{z^{3}}{(1 + x)(1 + y)}
\geq \frac{3}{4}.
\]](http://latex.artofproblemsolving.com/5/6/5/56568d27a296f1c900fabbb1042549cd2e552e29.png)
,![\[ \frac{a}{\sqrt{a^2 + 8bc}} + \frac{b}{\sqrt{b^2 + 8ca}} + \frac{c}{\sqrt{c^2 + 8ab}} \geq 1. \]](http://latex.artofproblemsolving.com/b/2/f/b2ff456632d4dd3b9ed93e4cba437bdd34d54cd8.png)
be a parallelogram of center 
.
,
and 
such that 
.
be given . On the extension of the segment 
beyond 
,
is chosen arbitrarily. Let the line through 
intersect the line 
at the point 
.
be the intersection of the lines 
and 
.
is tangent to the circumcircle of the triangle 
.
be any point. Let 
be projection point from 
.
cuts circumcircle 
at 
.
be antipode of 
are cyclic.
,
be real numbers, such that 
.
.
Y by Pengu14, Alex-131
hey!! im a first time applicant for a lot of math camps (namely: usa-canada mathcamp, PROMYS, Ross, MathILY, HCSSiM), and I was just wondering:
1. how much of an effect would being a first-time applicant have on making these math camps individually?
2. I spent a huge amount of effort (like 50 or something hours) on the USA-Canada Mathcamp application quiz in particular, but I'm pretty worried because supposedly almost no first-time applicants get into the camp. Are there any first-time applicants that you know of, and what did their applications (as in, qualifying quiz solutions) look like?
3. Additionally, a lot of people give off the impression that not doing the full problem set will screw your application over, except in rare cases. How much do you think a fakesolve would impact my PROMYS application chances?
thanks in advance!
1. how much of an effect would being a first-time applicant have on making these math camps individually?
2. I spent a huge amount of effort (like 50 or something hours) on the USA-Canada Mathcamp application quiz in particular, but I'm pretty worried because supposedly almost no first-time applicants get into the camp. Are there any first-time applicants that you know of, and what did their applications (as in, qualifying quiz solutions) look like?
3. Additionally, a lot of people give off the impression that not doing the full problem set will screw your application over, except in rare cases. How much do you think a fakesolve would impact my PROMYS application chances?
thanks in advance!
)
