why in sample input answer for test 2 is NO?
and if it is NO why answer for 3test 3 is YES?

is anybody here ?!

test#2 contains a point (0;0) which cannot belong to the inscribed square, that's obvious.

i don't understand why it's "yes" for the first variant

Square ABCD: A(2,0),B(0,2),C(-2,0),D(0,-2)
Sample 1 gives the middle point of AB and AD

"square of the foundation should be inscribed in the circle of the island" what does "inscribe" mean here? does it mean that the corners of square should lie on the circle?

yes, this is what the term "inscribed" means