<p>Alice is throwing <code>n</code> darts on a very large wall. You are given an array <code>darts</code> where <code>darts[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> is the position of the <code>i<sup>th</sup></code> dart that Alice threw on the wall.</p>

<p>Bob knows the positions of the <code>n</code> darts on the wall. He wants to place a dartboard of radius <code>r</code> on the wall so that the maximum number of darts that Alice throws lie&nbsp;on the dartboard.</p>

<p>Given the integer <code>r</code>, return <em>the maximum number of darts that can lie on the dartboard</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/04/29/sample_1_1806.png" style="width: 248px; height: 211px;" />
<pre>
<strong>Input:</strong> darts = [[-2,0],[2,0],[0,2],[0,-2]], r = 2
<strong>Output:</strong> 4
<strong>Explanation:</strong> Circle dartboard with center in (0,0) and radius = 2 contain all points.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/04/29/sample_2_1806.png" style="width: 306px; height: 244px;" />
<pre>
<strong>Input:</strong> darts = [[-3,0],[3,0],[2,6],[5,4],[0,9],[7,8]], r = 5
<strong>Output:</strong> 5
<strong>Explanation:</strong> Circle dartboard with center in (0,4) and radius = 5 contain all points except the point (7,8).
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= darts.length &lt;= 100</code></li>
	<li><code>darts[i].length == 2</code></li>
	<li><code>-10<sup>4</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>4</sup></code></li>
	<li>All the <code>darts</code>&nbsp;are unique</li>
	<li><code>1 &lt;= r &lt;= 5000</code></li>
</ul>

class Solution:
    from typing import List
    import math

    def numPoints(self, darts: List[List[int]], r: int) -> int:
        def get_circle_center(x1, y1, x2, y2, r):
            d = math.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2)
            if d > 2 * r:
                return []
            a = (x1 + x2) / 2
            b = (y1 + y2) / 2
            h = math.sqrt(r ** 2 - (d / 2) ** 2)
            dx = (y1 - y2) / d * h
            dy = (x2 - x1) / d * h
            return [(a + dx, b + dy), (a - dx, b - dy)]

        def count_points(center, points, r):
            count = 0
            for x, y in points:
                if math.sqrt((x - center[0]) ** 2 + (y - center[1]) ** 2) <= r + 1e-7:
                    count += 1
            return count

        if not darts:
            return 0

        max_points = 1
        for i in range(len(darts)):
            for j in range(i + 1, len(darts)):
                centers = get_circle_center(darts[i][0], darts[i][1], darts[j][0], darts[j][1], r)
                for center in centers:
                    max_points = max(max_points, count_points(center, darts, r))

        return max_points

16800