点到圆的最短距离

给定一个给定半径的圆，其圆心在坐标平面中的特定位置。在坐标平面中，给出了另一个点。任务是找到点和圆之间的最短距离。
例子：

Input: x1 = 4, y1 = 6, x2 = 35, y2 = 42, r = 5 
Output: 42.5079

Input: x1 = 0, y1 = 0, x2 = 5, y2 = 12, r = 3
Output: 10

方法：

• 让圆的半径 = r

• 圆心坐标 = (x1, y1)

• 点的坐标 = (x2, y2)

• 让中心与点之间的距离= d

• 由于线 AC 在 B 处与圆相交，所以最短距离将是 BC，
  等于(dr)

• 这里使用距离公式，
  d = √((x2-x1)^2 – (y2-y1)^2)

• 所以BC = √((x2-x1)^2 – (y2-y1)^2) – r

• 所以，
  $Shortest distance between the point and the circle = sqrt((x2-x1)^2 - (y2-y1)^2) - r$

下面是上述方法的实现：

C++

// C++ program to find
// the Shortest distance
// between a point and
// a circle
#include 
using namespace std;
 
// Function to find the shortest distance
void dist(double x1, double y1, double x2, double y2, double r)
{
    cout << "The shortest distance "
         << "between a point and a circle is "
         << sqrt((pow((x2 - x1), 2))
                 + (pow((y2 - y1), 2)))
                - r
         << endl;
}
 
// Driver code
int main()
{
    double x1 = 4, y1 = 6,
           x2 = 35, y2 = 42, r = 5;
    dist(x1, y1, x2, y2, r);
    return 0;
}

Java

// Java program to find
// the Shortest distance
// between a point and
// a circle
class GFG
{
 
// Function to find the shortest distance
static void dist(double x1, double y1, double x2,
                                double y2, double r)
{
    System.out.println("The shortest distance "
            + "between a point and a circle is "
            + (Math.sqrt((Math.pow((x2 - x1), 2))
                    + (Math.pow((y2 - y1), 2)))
            - r));
}
 
// Driver code
public static void main(String[] args)
{
    double x1 = 4, y1 = 6,
            x2 = 35, y2 = 42, r = 5;
    dist(x1, y1, x2, y2, r);
}
}
 
/* This code contributed by PrinciRaj1992 */

Python3

# Python program to find
# the Shortest distance
# between a point and
# a circle
  
# Function to find the shortest distance
def dist(x1, y1, x2, y2, r):
    print("The shortest distance between a point and a circle is "
    ,((((x2 - x1)** 2) + ((y2 - y1)** 2))**(1/2)) - r);
 
  
# Driver code
x1 = 4;
y1 = 6;
x2 = 35;
y2 = 42;
r = 5;
dist(x1, y1, x2, y2, r);
 
 
# This code has been contributed by 29AjayKumar

C#

// C# program to find the Shortest distance
// between a point and a circle
using System;
 
class GFG
{
 
// Function to find the shortest distance
static void dist(double x1, double y1, double x2,
                                double y2, double r)
{
    Console.WriteLine("The shortest distance "
            + "between a point and a circle is "
            + (Math.Sqrt((Math.Pow((x2 - x1), 2))
                    + (Math.Pow((y2 - y1), 2)))
            - r));
}
 
// Driver code
public static void Main(String[] args)
{
    double x1 = 4, y1 = 6,
            x2 = 35, y2 = 42, r = 5;
    dist(x1, y1, x2, y2, r);
}
}
 
/* This code contributed by PrinciRaj1992 */

Javascript

 
// javascript program to find
// the Shortest distance
// between a povar and
// a circle
 
// Function to find the shortest distance
function dist(x1 , y1 , x2, y2 , r)
{
    document.write("The shortest distance "
            + "between a povar and a circle is "
            + (Math.sqrt((Math.pow((x2 - x1), 2))
                    + (Math.pow((y2 - y1), 2)))
            - r).toFixed(5));
}
 
// Driver code
 
 
var x1 = 4, y1 = 6,
        x2 = 35, y2 = 42, r = 5;
dist(x1, y1, x2, y2, r);
 
 
// This code contributed by Princi Singh
 

输出：

The shortest distance between a point and a circle is 42.5079

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