# Check if a line touches or intersects a circle

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.

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++

`// 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 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; ` `} ` |

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## 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. ` |

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## 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 ` |

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## 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. ` |

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## PHP

`<?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 ` `?> ` |

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**Output :**

Touch

This article is contributed by **Anuj Chauhan**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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