of integers satisfying![\[x_0 = 0, |x_n| = |x_{n-1} + 1|\]](http://latex.artofproblemsolving.com/4/8/e/48e7b6f98f2062879377a9a2e507a63eac9269a8.png)
.
.
,
and 
and so forth.
.
be a tetrahedron such that 
A sphere of radius 
is circumscribed about tetrahedron 
Given that 
,
,
,![$$r^2+\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \ge \frac{9\sqrt[3]{4}}{4}$$](http://latex.artofproblemsolving.com/6/c/6/6c665b4611f5fc8ebeba03ac649bfee4e2634950.png)
with equality at ![$a=b=c=\sqrt[3]{2}.$](http://latex.artofproblemsolving.com/b/b/9/bb9c9671b23cb45e5f85ae01bf25d566c2e43e91.png)
and 
be points on a plane such that 
,
is a positive integer. Let 
be the set of all points 
such that 
,
is a real number. The path that 
Y by
As shown in the picture,
is mirror image similar to 
,
,
are on the outside of quadrilateral 
. 
is on 
,
is on 
and 
,
and 
intersect at .Prove that: 
is mirror image similar to 
,
,
are on the outside of quadrilateral 
. 
is on 
,
is on 
and 
,
and 
intersect at .Prove that: 
Attachments:
