[/quote]
,
with 
.
and 
are on 
and 
respectively such that 
.
and 
meet at 
.
is the incenter of 
and 
is the orthocenter of 
.
and 
are circles with diameter 
and 
,
and 
.
.
,
,
,
be non-negative real numbers such that![\[2a+2b+2c+2d+ab+bc+cd+da+3=abcd.\]](http://latex.artofproblemsolving.com/d/e/8/de8ccd816cfe032a97d940982192b1abea21dc18.png)
prove that : ![\[\sqrt[4]{abc}+\sqrt[4]{bcd}+\sqrt[4]{cda}+\sqrt[4]{dab}\le\sqrt[4]{27(1+a)(1+b)(1+c)(1+d)}.\]](http://latex.artofproblemsolving.com/a/f/c/afc556cd8f5c7f4dedf153ffb92fb1f978c56823.png)
such that 
is a perfect square.
is the number of primes that are not bigger than 
.
we have 
.
be a positive integer. Find the maximum number of diagonals in a regular 
.
at 
and have center 
.
be the midpoint of arc 
on the circumcircle. Suppose quadrilateral 
is cyclic such that 
lies on 
.
.
be a semicircle with diameter 
.
be a point on 
and 
.
touches 
,
in a point 
.
touches 
and 
and 
where 
.
Y by Adventure10
Heres the problem :
"The dimensions of 2 boxes are A by B by C, and D by E by F, respectively. If A<C, D<B, E<A, B<E, and A<F, what is the diameter of the largest largest ball that can fit into both boxes? Express your answer in terms of A,B,C,D,E,F, and/or F"
"The dimensions of 2 boxes are A by B by C, and D by E by F, respectively. If A<C, D<B, E<A, B<E, and A<F, what is the diameter of the largest largest ball that can fit into both boxes? Express your answer in terms of A,B,C,D,E,F, and/or F"
