and the sets 
If 
has exactly three elements, prove that 
cannot be an integer.
satisfy:
![$[(x-2)^2+(y-4)^2][ (x-1)^2 + (y-2)^2] = 36$](http://latex.artofproblemsolving.com/b/1/0/b108dc2cac5b7491fb83418eb36c7184f6d5d30c.png)
such that
holds for all 
.
such that:
with all 
Y by
Determine the greatest possible value of the constant 
that satisfies the following condition: for any convex heptagon the sum of the lengthes of all it’s diagonals is greater than 
, where 
is the perimeter of the heptagon.
(I. Zhuk)
that satisfies the following condition: for any convex heptagon the sum of the lengthes of all it’s diagonals is greater than 
, where 
is the perimeter of the heptagon.(I. Zhuk)
This post has been edited 3 times. Last edited by parmenides51, Dec 27, 2020, 6:54 AM
