M:x2+y2=1center=(0,0)
N:x2+y2−2x=0,center=(1,0)
O:x2+y2−2x−2y+1=0,center=(1,1)
P:x2+y2−2y=0,center=(0,1)

MN=(1−0)2+(0−0)2=1
NO=(1−1)2+(0−1)2=1
OP=(1−0)2+(1−1)2=1
PM=(0−1)2+(1−1)2=1
Then, all the sides are equal of a quadrilateral then MNOP is a square.