text: from collections import namedtuple
  import math
  
  Circle = namedtuple('Circle', 'x, y, r')
  
  def solveApollonius(c1, c2, c3, s1, s2, s3):
      '''
      solveApollonius((0, 0, 1), (4, 0, 1), (2, 4, 2), 1,1,1)
      Circle(x=2.0, y=2.1, r=3.9)
      solveApollonius((0, 0, 1), (4, 0, 1), (2, 4, 2), -1,-1,-1)
      Circle(x=2.0, y=0.8333333333333333, r=1.1666666666666667)
      '''
      x1, y1, r1 = c1
      x2, y2, r2 = c2
      x3, y3, r3 = c3
  
      v11 = 2*x2 - 2*x1
      v12 = 2*y2 - 2*y1
      v13 = x1*x1 - x2*x2 + y1*y1 - y2*y2 - r1*r1 + r2*r2
      v14 = 2*s2*r2 - 2*s1*r1
  
      v21 = 2*x3 - 2*x2
      v22 = 2*y3 - 2*y2
      v23 = x2*x2 - x3*x3 + y2*y2 - y3*y3 - r2*r2 + r3*r3
      v24 = 2*s3*r3 - 2*s2*r2
  
      w12 = v12/v11
      w13 = v13/v11
      w14 = v14/v11
  
      w22 = v22/v21-w12
      w23 = v23/v21-w13
      w24 = v24/v21-w14
  
      P = -w23/w22
      Q = w24/w22
      M = -w12*P-w13
      N = w14 - w12*Q
  
      a = N*N + Q*Q - 1
      b = 2*M*N - 2*N*x1 + 2*P*Q - 2*Q*y1 + 2*s1*r1
      c = x1*x1 + M*M - 2*M*x1 + P*P + y1*y1 - 2*P*y1 - r1*r1
  
      # Find a root of a quadratic equation. This requires the circle centers not to be e.g. colinear
      D = b*b-4*a*c
      rs = (-b-math.sqrt(D))/(2*a)
  
      xs = M+N*rs
      ys = P+Q*rs
  
      return Circle(xs, ys, rs)
  
  if __name__ == '__main__':
      c1, c2, c3 = Circle(0, 0, 1), Circle(4, 0, 1), Circle(2, 4, 2)
      print((solveApollonius(c1, c2, c3, 1, 1, 1)))    #Expects "Circle[x=2.00,y=2.10,r=3.90]" (green circle in image)
      print((solveApollonius(c1, c2, c3, -1, -1, -1))) #Expects "Circle[x=2.00,y=0.83,r=1.17]" (red circle in image)
  