# 1401. Circle and Rectangle Overlapping

<https://leetcode.com/problems/circle-and-rectangle-overlapping>

## Description

Given a circle represented as (`radius`, `x_center`, `y_center`) and an axis-aligned rectangle represented as (`x1`, `y1`, `x2`, `y2`), where (`x1`, `y1`) are the coordinates of the bottom-left corner, and (`x2`, `y2`) are the coordinates of the top-right corner of the rectangle.

Return True if the circle and rectangle are overlapped otherwise return False.

In other words, check if there are **any** point (xi, yi) such that belongs to the circle and the rectangle at the same time.

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/02/20/sample_4_1728.png)

```
**Input:** radius = 1, x\_center = 0, y\_center = 0, x1 = 1, y1 = -1, x2 = 3, y2 = 1
**Output:** true
**Explanation:** Circle and rectangle share the point (1,0) 
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2020/02/20/sample_2_1728.png)

```
**Input:** radius = 1, x\_center = 0, y\_center = 0, x1 = -1, y1 = 0, x2 = 0, y2 = 1
**Output:** true
```

**Example 3:**

![](https://assets.leetcode.com/uploads/2020/03/03/sample_6_1728.png)

```
**Input:** radius = 1, x\_center = 1, y\_center = 1, x1 = -3, y1 = -3, x2 = 3, y2 = 3
**Output:** true
```

**Example 4:**

```
**Input:** radius = 1, x\_center = 1, y\_center = 1, x1 = 1, y1 = -3, x2 = 2, y2 = -1
**Output:** false
```

**Constraints:**

* `1 <= radius <= 2000`
* `-10^4 <= x_center, y_center, x1, y1, x2, y2 <= 10^4`
* `x1 < x2`
* `y1 < y2`

## ac

```java
```


---

# 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://jaywin.gitbook.io/leetcode/solutions/1401-circle-and-rectangle-overlapping.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.