# Maximum Number of Darts Inside of a Circular Dartboard

You have a very large square wall and a circular dartboard placed on the wall. You have been challenged to throw darts into the board blindfolded. Darts thrown at the wall are represented as an array of `points` on a 2D plane. 

Return the maximum number of points that are within or lie on **any** circular dartboard of radius `r`.

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/04/29/sample_1_1806.png)

```
Input: points = [[-2,0],[2,0],[0,2],[0,-2]], r = 2
Output: 4
Explanation: Circle dartboard with center in (0,0) and radius = 2 contain all points.
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2020/04/29/sample_2_1806.png)

```
Input: points = [[-3,0],[3,0],[2,6],[5,4],[0,9],[7,8]], r = 5
Output: 5
Explanation: Circle dartboard with center in (0,4) and radius = 5 contain all points except the point (7,8).
```

**Example 3:**

```
Input: points = [[-2,0],[2,0],[0,2],[0,-2]], r = 1
Output: 1
```

**Example 4:**

```
Input: points = [[1,2],[3,5],[1,-1],[2,3],[4,1],[1,3]], r = 2
Output: 4
```

**Constraints:**

* `1 <= points.length <= 100`
* `points[i].length == 2`
* `-10^4 <= points[i][0], points[i][1] <= 10^4`
* `1 <= r <= 5000`

```java
// http://mathforum.org/library/drmath/view/53027.html
class Solution {
    public int numPoints(int[][] points, int r) {
        int max = 0;
        // If we take every point as center
        for (int i = 0; i < points.length; i++) {
            int count = 0;
            for (int j = 0; j < points.length; j++) {
                if (Math.pow(points[j][0] - points[i][0], 2) + Math.pow(points[j][1] - points[i][1], 2) <= r * r)
                    count++;
            }
            max = Math.max(max, count);
        }
        // If the 2 points are are taken at circumference
        for (int i = 0; i < points.length; i++) {
            for (int j = i + 1; j < points.length; j++) {
                if (Math.pow(points[j][0] - points[i][0], 2) + Math.pow(points[j][1] - points[i][1], 2) > 4 * r * r)
                    continue;
                double q = Math.sqrt(Math.pow(points[j][0] - points[i][0], 2) + Math.pow(points[j][1] - points[i][1], 2));
                double x3 = (double) (points[i][0] + points[j][0]) / 2;
                double y3 = (double) (points[i][1] + points[j][1]) / 2;
                double centerX1 = x3 + Math.sqrt(r * r - q * q / 4) * (points[i][1] - points[j][1]) / q;
                double centerY1 = y3 + Math.sqrt(r * r - q * q / 4) * (points[j][0] - points[i][0]) / q;
                double centerX2 = x3 - Math.sqrt(r * r - q * q / 4) * (points[i][1] - points[j][1]) / q;
                double centerY2 = y3 - Math.sqrt(r * r - q * q / 4) * (points[j][0] - points[i][0]) / q;
                int circleOneCount = 0, circleTwoCount = 0;
                for (int k = 0; k < points.length; k++) {
                    if (Math.pow(centerX1 - points[k][0], 2) + Math.pow(centerY1 - points[k][1], 2) <= r * r)
                        circleOneCount++;
                    if (Math.pow(centerX2 - points[k][0], 2) + Math.pow(centerY2 - points[k][1], 2) <= r * r)
                        circleTwoCount++;
                }
                max = Math.max(max, Math.max(circleOneCount, circleTwoCount));
            }
        }
        return max;
    }
}
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://mayanktyagi3111.gitbook.io/interview-prep/geometry/maximum-number-of-darts-inside-of-a-circular-dartboard.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.