用公式直接求解

def get_circle(self, p0, p1, r):
    if p1[0] == p0[0]:
        y0 = y1 = (p0[1]+p1[1]) / 2
        deltay = (y0-p0[1]) ** 2
        deltax = sqrt(r ** 2 - deltay)
        x0 = p1[0] - deltax
        x1 = p1[0] + deltax
    else:
        C1 = (p1[0]**2 + p1[1]**2 - p0[0]**2 - p0[1]**2) / 2 / (p1[0] - p0[0])
        C2 = (p1[1] - p0[1]) / (p1[0] - p0[0])
        A = 1 + C2**2
        B = 2 * (p0[0] - C1) * C2 - 2*p0[1]
        C = (p0[0]-C1)**2 + p0[1]**2 - r**2
        y0 = (-B + sqrt(B*B - 4 * A * C)) / 2 / A
        y1 = (-B - sqrt(B*B - 4 * A * C)) / 2 / A
        x0 = C1 - C2 * y0
        x1 = C1 - C2 * y1
    return [x0, y0], [x1, y1]

leetcode 5415. 圆形靶内的最大飞镖数量

from math import sqrt
class Solution:
    def get_dis(self, p0, p1):
        return (p0[0]-p1[0])**2 + (p0[1]-p1[1])**2

    def get_circle(self, p0, p1, r):
        if p1[0] == p0[0]:
            y0 = y1 = (p0[1]+p1[1]) / 2
            deltay = (y0-p0[1]) ** 2
            deltax = sqrt(r ** 2 - deltay)
            x0 = p1[0] - deltax
            x1 = p1[0] + deltax
        else:
            C1 = (p1[0]**2 + p1[1]**2 - p0[0]**2 - p0[1]**2) / 2 / (p1[0] - p0[0])
            C2 = (p1[1] - p0[1]) / (p1[0] - p0[0])
            A = 1 + C2**2
            B = 2 * (p0[0] - C1) * C2 - 2*p0[1]
            C = (p0[0]-C1)**2 + p0[1]**2 - r**2
            y0 = (-B + sqrt(B*B - 4 * A * C)) / 2 / A
            y1 = (-B - sqrt(B*B - 4 * A * C)) / 2 / A
            x0 = C1 - C2 * y0
            x1 = C1 - C2 * y1
        return [x0, y0], [x1, y1]

    def get_number(self, points, circle, r_squre):
        res = 0
        for p in points:
            dis = self.get_dis(p, circle)
            # print(dis, r_squre)
            if dis <= r_squre:
                res += 1
        return res


    def numPoints(self, points: [[int]], r: int) -> int:
        res = 0
        r_squre = r**2
        for i in range(len(points)):
            for j in range(i+1, len(points)):
                dis = self.get_dis(points[i], points[j])
                if dis > r_squre*4:
                    res = max(res, 1)
                else:
                    # print(points[i], points[j])
                    circle1, circle2 = self.get_circle(points[i], points[j], r)
                    # print("圆心", circle1, circle2)
                    res = max(res,
                            self.get_number(points, circle1, r_squre), 
                            self.get_number(points, circle2, r_squre)
                            )
        return res


# if __name__ == '__main__':
#     points = [[-3,0],[3,0],[2,6],[5,4],[0,9],[7,8]]
#     r = 5
#     points = [[1,2],[3,5],[1,-1],[2,3],[4,1],[1,3]]
#     r = 2
#     points = [[-2,0],[2,0],[0,2],[0,-2]]
#     r = 1
#     points = [[-2,0],[2,0],[0,2],[0,-2]]
#     r = 2
#     print(Solution().get_number(points, [0,4], r**2))
#     print(Solution().get_circle([2,4],[4,2],2))
#     print(Solution().get_circle([2,4],[4,4],3))
#     print(Solution().get_circle([2,4],[2,0],2))
#     # print(Solution().get_dis(points[0], points[5]))
#     print(Solution().numPoints(points, r))