wild dogs check | Python Fiddle

import sympy
from sympy import Point, Line
from datetime import datetime
import time

def wild_dogs(coords): 
    start_time = datetime.now()
    p_zero = Point(0, 0)
    points = []
    mass_points = []
    
    for i in range(len(coords)):
        points.append(Point(coords[i][0], coords[i][1]))
        for j in range(len(coords)):
            if Point(coords[j][0], coords[j][1]) not in points and i!=j:
                if Point.is_collinear(*points, Point(coords[j][0], coords[j][1])): 
                    points.append(Point(coords[j][0], coords[j][1]))
                else:
                    for k in points:
                        if Point.is_collinear(k, Point(coords[j][0], coords[j][1])) and [k, Point(coords[j][0], coords[j][1])] not in mass_points:
                            mass_points.append([k, Point(coords[j][0], coords[j][1])])
        mass_points.append(points[:])
        points.clear()  
    result = []
    for i in mass_points:         
        a=Line(*i).distance(p_zero)
        result.append([len(i), round(sympy.N(a), 2)])
    print(datetime.now() - start_time)
    return float(sorted(result, key = lambda x: (-x[0], x[1]))[0][1])
"""    
import collections
def wild_dogs(coords):
    start_time = datetime.now()
    slope_dogs=[]
    dist_target=[]
    min_dist=[]
    for i in range(len(coords)):
        for j in range(len(coords)):
            if i!=j and (coords[i][0]-coords[j][0])!=0:
                #print(coords[i][0])
                slope_dogs.append(round((coords[i][1]-coords[j][1])/(coords[i][0]-coords[j][0]),2))
        print(slope_dogs)
        for slope in slope_dogs:
            dist_target.append(round(abs(coords[i][1]-slope*coords[i][0])/(slope**2+1)**0.5,2))
        print(dist_target)
    for coll in collections.Counter(dist_target).most_common():
        if coll[1]==max(collections.Counter(dist_target).most_common(), key = lambda tup : tup[1])[1]:
            min_dist.append(coll[0])
    print(min(min_dist))
    print(datetime.now() - start_time)
    return min(min_dist)
"""
if __name__ == '__main__':
    print("Example:")
    print(wild_dogs([[6,-0.5],[3,-5], [34,54], [24,75] ,[1,-20], [23,12]]))
    #print(wild_dogs([(6, -0.5), (3, -5), (1, -20)]))

#These "asserts" using only for self-checking and not necessary for auto-testing
    """assert wild_dogs([(7, 122), (8, 139), (9, 156), 
                      (10, 173), (11, 190), (-100, 1)]) == 0.18

assert wild_dogs([(6, -0.5), (3, -5), (1, -20)]) == 3.63

assert wild_dogs([(10, 10), (13, 13), (21, 18)]) == 0"""

print("Coding complete? Click 'Check' to earn cool rewards!")

Python Fiddle

Python Cloud IDE