leetcode-problemset/leetcode-cn/problem (Chinese)/圆和矩形是否有重叠 [circle-and-rectangle-overlapping].html

<p>给你一个以 (<code>radius</code>, <code>x_center</code>, <code>y_center</code>) 表示的圆和一个与坐标轴平行的矩形 (<code>x1</code>, <code>y1</code>, <code>x2</code>, <code>y2</code>)，其中&nbsp;(<code>x1</code>, <code>y1</code>) 是矩形左下角的坐标，(<code>x2</code>, <code>y2</code>) 是右上角的坐标。</p>

<p>如果圆和矩形有重叠的部分，请你返回 True ，否则返回 False&nbsp;。</p>

<p>换句话说，请你检测是否 <strong>存在</strong> 点&nbsp;(xi, yi) ，它既在圆上也在矩形上（两者都包括点落在边界上的情况）。</p>

<p>&nbsp;</p>

<p><strong>示例 1：</strong></p>

<p><img alt="" src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/04/04/sample_4_1728.png" style="height: 167px; width: 258px;"></p>

<pre><strong>输入：</strong>radius = 1, x_center = 0, y_center = 0, x1 = 1, y1 = -1, x2 = 3, y2 = 1
<strong>输出：</strong>true
<strong>解释：</strong>圆和矩形有公共点 (1,0) 
</pre>

<p><strong>示例 2：</strong></p>

<p><strong><img alt="" src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/04/04/sample_2_1728.png" style="height: 135px; width: 150px;"></strong></p>

<pre><strong>输入：</strong>radius = 1, x_center = 0, y_center = 0, x1 = -1, y1 = 0, x2 = 0, y2 = 1
<strong>输出：</strong>true
</pre>

<p><strong>示例 3：</strong></p>

<p><strong><img alt="" src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/04/04/sample_6_1728.png" style="height: 165px; width: 175px;"></strong></p>

<pre><strong>输入：</strong>radius = 1, x_center = 1, y_center = 1, x1 = -3, y1 = -3, x2 = 3, y2 = 3
<strong>输出：</strong>true
</pre>

<p><strong>示例 4：</strong></p>

<pre><strong>输入：</strong>radius = 1, x_center = 1, y_center = 1, x1 = 1, y1 = -3, x2 = 2, y2 = -1
<strong>输出：</strong>false
</pre>

<p>&nbsp;</p>

<p><strong>提示：</strong></p>

<ul>
	<li><code>1 &lt;= radius &lt;= 2000</code></li>
	<li><code>-10^4 &lt;= x_center, y_center, x1, y1, x2, y2 &lt;= 10^4</code></li>
	<li><code>x1 &lt; x2</code></li>
	<li><code>y1 &lt; y2</code></li>
</ul>