,
to be the set of all triplets 
of natural numbers, with 
odd and 
,
and 
.
for which 
be positive real numbers . Prove that
and 
in the plane, draws the perpendicular bisector of 
.
Y by Adventure10, Mango247
Peter is a pentacrat and spends his time drawing pentagrams.
With the abbreviation
for the area of an arbitrary triangle 
, he notes that any convex pentagon 
satisfies the equality
.
Guess what you are supposed to do and do it.
With the abbreviation
for the area of an arbitrary triangle 
, he notes that any convex pentagon 
satisfies the equality
.Guess what you are supposed to do and do it.
![$[XYZ] = \frac{xyz}{4R}$](http://latex.artofproblemsolving.com/1/c/b/1cbaf9d1539d98fad84b7fb93f46833d397e7c31.png)
here 
are the sides and the circumradius of 
,
.
be a convex cyclic quadrilateral. Let 
,
,
.
