Cross points of a circle and a line in python

def project(an,p10):
  p12=an[1]-an[0]
  norm = np.linalg.norm(p12)**2
  #print(norm)
  ret = np.dot(p10,p12)/norm
  #print(ret)
  return an[0]+p12*ret

def getCrossPoints(c, r, l): 
  #print(l)
  pr = project(l, c)
  #print(pr)
  e = (l[1]-l[0]) / (np.linalg.norm(l[1]-l[0]))
  mid = (r*r - np.linalg.norm(pr-c)**2)
  base = np.sqrt(mid)
  #print("==e,base==")
  #print(mid,e,base)
  return [pr-e*base, pr+e*base]

a = []
a.append(map(int, raw_input().split()))
for aa in a:
    cx = aa[0]
    cy = aa[1]
    r = aa[2]
    c = np.array([cx,cy])

n = input()
for i in range(n):
  a = []
  a.append(map(int, raw_input().split()))
  for aa in a:
    hn = np.array(aa).reshape(2,2)
    s1 = np.array([hn[0][0],hn[0][1]])
    s2 = np.array([hn[1][0],hn[1][1]])
    #print(c,r,s1,s2)
    gcp = getCrossPoints(c, r, [s1,s2])
    #print(gcp)
    out = ""
    for x in gcp:
        for xx in x:
            if (out):
                out = out + " " 
            out = out + str(xx)
    print(out)

2 1 1
2
0 1 4 1
1.0 1.0 3.0 1.0
3 0 3 3
3.0 1.0 3.0 1.0

Refs.

• projection
• sqrt