检查一条线是否与圆相交或相交

给定圆心坐标和半径 > 1 和直线方程。任务是检查给定的线是否与圆相撞。有三种可能：

1. 线与圆相交。
2. 线触及圆。
3. 线在圆外。

注：一条直线的一般方程为 a*x + b*y + c = 0，所以输入中只给出常数 a、b、c。
例子 ：

Input : radius = 5, center = (0, 0), 
        a = 1, b = -1, c = 0.
Output : Intersect

Input :  radius = 5, center = (0, 0), 
         a = 5, b = 0, c = 0.
Output : Touch

Input : radius = 5, center = (0, 0),
         a = 1, b = 1, c = -16.
Output : Outside

这个想法是将圆心和线之间的垂直距离与圆的半径进行比较。
算法：
1. 找到圆心和给定直线之间的垂线（比如 p）。
2. 将此距离 p 与半径 r 进行比较。
……a) 如果 p > r，则线位于圆外。
……b) 如果 p = r，则线接触圆。
……c) 如果 p < r，则线与圆相交。
如何求垂直距离？
线到点的距离可以使用以下公式计算：
$\frac{ax_{0}+by_{0}+c}{\sqrt{a^{2}+b^{2}}}$
有关上述公式的详细信息，请参阅 Wiki。

C++

// CPP program to check if a line touches or
// intersects or outside a circle.
#include 
using namespace std;
 
void checkCollision(int a, int b, int c,
                  int x, int y, int radius)
{
    // Finding the distance of line from center.
    int dist = (abs(a * x + b * y + c)) /
                     sqrt(a * a + b * b);
 
    // Checking if the distance is less than,
    // greater than or equal to radius.
    if (radius == dist)
        cout << "Touch" << endl;
    else if (radius > dist)
        cout << "Intersect" << endl;
    else
        cout << "Outside" << endl;
}
 
// Driven Program
int main()
{
    int radius = 5;
    int x = 0, y = 0;
    int a = 3, b = 4, c = 25;
    checkCollision(a, b, c, x, y, radius);
    return 0;
}

Java

// Java program to check if a line touches or
// intersects or outside a circle.
 
import java.io.*;
 
class GFG {
     
    static void checkCollision(int a, int b, int c,
                               int x, int y, int radius)
    {
        // Finding the distance of line from center.
        double dist = (Math.abs(a * x + b * y + c)) /
                        Math.sqrt(a * a + b * b);
     
        // Checking if the distance is less than,
        // greater than or equal to radius.
        if (radius == dist)
            System.out.println ( "Touch" );
        else if (radius > dist)
            System.out.println( "Intersect") ;
        else
            System.out.println( "Outside") ;
    }
     
    // Driven Program
    public static void main (String[] args)
    {
        int radius = 5;
        int x = 0, y = 0;
        int a = 3, b = 4, c = 25;
        checkCollision(a, b, c, x, y, radius);
     
    }
}
 
// This article is contributed by vt_m.

Python3

# python program to check if a line
# touches or  intersects or outside
# a circle.
 
import math
 
def checkCollision(a, b, c, x, y, radius):
     
    # Finding the distance of line
    # from center.
    dist = ((abs(a * x + b * y + c)) /
            math.sqrt(a * a + b * b))
 
    # Checking if the distance is less
    # than, greater than or equal to radius.
    if (radius == dist):
        print("Touch")
    elif (radius > dist):
        print("Intersect")
    else:
        print("Outside")
 
# Driven Program
radius = 5
x = 0
y = 0
a = 3
b = 4
c = 25
checkCollision(a, b, c, x, y, radius)
 
# This code is contributed by Sam007

C#

// C# program to check if a line touches or
// intersects or outside a circle.
using System;
 
class GFG {
     
    static void checkCollision(int a, int b, int c,
                            int x, int y, int radius)
    {
        // Finding the distance of line from center.
        double dist = (Math.Abs(a * x + b * y + c)) /
                        Math.Sqrt(a * a + b * b);
     
        // Checking if the distance is less than,
        // greater than or equal to radius.
        if (radius == dist)
            Console.WriteLine ("Touch");
        else if (radius > dist)
            Console.WriteLine("Intersect");
        else
            Console.WriteLine("Outside");
    }
     
    // Driven Program
    public static void Main ()
    {
        int radius = 5;
        int x = 0, y = 0;
        int a = 3, b = 4, c = 25;
         
        checkCollision(a, b, c, x, y, radius);
     
    }
}
 
// This article is contributed by vt_m.

PHP

 $dist)
        echo "Intersect";
    else
        echo "Outside" ;
}
 
// Driver Code
$radius = 5;
$x = 0;
$y = 0;
$a = 3;
$b = 4;
$c = 25;
checkCollision($a, $b, $c, $x, $y, $radius);
 
// This code is contributed by Sam007
?>

Javascript

 
// JavaScript program to check if a line touches or
// intersects or outside a circle.
 
function checkCollision(a, b, c, x, y, radius)
    {
     
        // Finding the distance of line from center.
        let dist = (Math.abs(a * x + b * y + c)) /
                        Math.sqrt(a * a + b * b);
       
        // Checking if the distance is less than,
        // greater than or equal to radius.
        if (radius == dist)
            document.write ( "Touch" );
        else if (radius > dist)
            document.write( "Intersect") ;
        else
            document.write( "Outside") ;
    }
 
// Driver Code
        let radius = 5;
        let x = 0, y = 0;
        let a = 3, b = 4, c = 25;
        checkCollision(a, b, c, x, y, radius);
 
// This code is contributed by susmitakundugoaldanga.

输出 ：

Touch

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