import numpy as np

def threepoint(p1, p2, p3):
    x1 = p1[0]
    x2 = p2[0]
    x3 = p3[0]
    
    y1 = p1[1]
    y2 = p2[1]
    y3 = p3[1]
    
    a = np.linalg.det(np.array([[x1, y1, 1], [x2, y2, 1], [x3, y3, 1]]))
    d = -np.linalg.det(np.array([[x1*x1+y1*y1, y1, 1], [x2*x2+y2*y2, y2, 1], [x3*x3+y3*y3, y3, 1]]))
    e = np.linalg.det(np.array([[x1*x1+y1*y1, x1, 1], [x2*x2+y2*y2, x2, 1], [x3*x3+y3*y3, x3, 1]]))
    f = -np.linalg.det(np.array([[x1*x1+y1*y1, x1, y1], [x2*x2+y2*y2, x2, y2], [x3*x3+y3*y3, x3, y3]]))
    
    x0 = -d/(2*a)
    y0 = -e/(2*a)
    r = np.sqrt((d*d+e*e)/(4*a*a)-f/a)
    
    return x0, y0, r