AoPS Academy
with 
. Denote the orthocenter of 
as 
, the intersection of 
and 
as 
. Compute the length of 
.
be a Chebyshev polynomial of the second kind. If n>2 and x > 2 is a integer, Could 
be a prime number?
, the following 
statements are equivalent:
is differentiable, with continuous first derivative.
and for any two sequences 
, convergent to 
, such that 
for any positive integer 
, the sequence 
is convergent.
![\[F(x)=\int\limits_0^{x}\left(\sin\frac 1t\right)^4\mathrm dt.\]](http://latex.artofproblemsolving.com/1/c/2/1c2359167d0bfb8af7d7e1f93984c195e5fb1971.png)
Determine the value of 
be two matrices such that 
. Prove that: is odd, then 
;
, then .
cm are given points A,B with 
cm and 
is a midpoint of 
. What is the perpendicular distance from to the circle?
isomorphic to 
?
![\[
\frac{2a^2}{(b-c)^2} + \frac{2b^2}{(a-c)^2} + \frac{2c^2}{(b-a)^2} \geq 2 + \sum \left| \frac{(a+b-c)(b+c-a)}{(c-a)^2} \right|
\]](http://latex.artofproblemsolving.com/4/8/1/4813b0f718b56d880792297a5fe6141ad2e1f2ab.png)
.
