import math
import numpy as np

x1 = int(input("Enter x-coordinate of point 1: "))
y1 = int(input("Enter y-coordinate of point 1: "))

x2 = int(input("Enter x-coordinate of point 2: "))
y2 = int(input("Enter y-coordinate of point 2: "))

x3 = int(input("Enter x-coordinate of point 3: "))
y3 = int(input("Enter y-coordinate of point 3: "))

a = np.array([(x1,y1,1),(x2,y2,1),(x3,y3,1)])
d = np.array([(((x1**2)+(y1**2)),y1,1), (((x2**2)+(y2**2)),y2,1), (((x3**2)+(y3**2)),y3,1)])
e = np.array([(((x1**2)+(y1**2)),x1,1), (((x2**2)+(y2**2)),x2,1), (((x3**2)+(y3**2)),x3,1)])
f = np.array([(((x1**2)+(y1**2)),x1,y1), (((x2**2)+(y2**2)),x2,y2), (((x3**2)+(y3**2)),x3,y3)])

A = np.linalg.det(a)
d1 = -np.linalg.det(d)
e1 = np.linalg.det(e)
f1 = -np.linalg.det(f)

h = round(((-d1)/(2*A)),2)
k = round(((-e1)/(2*A)),2)

r = round((math.sqrt(((d1**2)+(e1**2)-(4*A*f1))/(4*(A**2)))),2)

D = round((d1/A),2)
E = round((e1/A),2)
F = round((f1/A),2)

center = (h,k)
vector = [D,E,F]

print("center", center)
print("radius", r)
print("vector", vector)