Check if a line touches or intersects a circle - GeeksforGeeks

24 Nov, 2021
Given coordinate of the center and radius > 1 of a circle and the equation of a line. The task is to check if the given line collide with the circle or not. There are three possibilities :  
Line intersect the circle.Line touches the circle.Line is outside the circle.
Line intersect the circle.
Line touches the circle.
Line is outside the circle.
 
Note: General equation of a line is a*x + b*y + c = 0, so only constant a, b, c are given in the input.Examples :  
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
 
The idea is to compare the perpendicular distance between center of circle and line with the radius of the circle.Algorithm: 1. Find the perpendicular (say p) between center of circle and given line. 2. Compare this distance p with radius r. ......a) If p > r, then line lie outside the circle. ......b) If p = r, then line touches the circle. ......c) If p < r, then line intersect the circle.How to find the perpendicular distance ? Distance of a line from a point can be computed using below formula:Refer Wiki for details of above formula.  
C++
Java
Python3
C#
PHP
Javascript
// CPP program to check if a line touches or // intersects or outside a circle.#include <bits/stdc++.h>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 Programint 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 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.
# 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 Programradius = 5x = 0y = 0a = 3b = 4c = 25checkCollision(a, b, c, x, y, radius)  # This code is contributed by Sam007
// 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// PHP 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.    $dist = (abs($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 == $dist)        echo "Touch";    else if ($radius > $dist)        echo "Intersect";    else        echo "Outside" ;}  // Driver Code$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?>
<script>  // 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.</script>
Output :  
Touch
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