# Check if two given circles touch or intersect each other

There are two circles A and B with their centres C1(x1, y1) and C2(x2, y2) and radius R1 and R2. The task is to check both circles A and B touch each other or not.

Examples :

Input : C1 = (3,  4)
C2 = (14, 18)
R1 = 5, R2 = 8
Output : Circles do not touch each other.

Input : C1 = (2,  3)
C2 = (15, 28)
R1 = 12, R2 = 10
Output : Circles intersect with each other.

Input : C1 = (-10,  8)
C2 = (14, -24)
R1 = 30, R2 = 10

Approach:
Distance between centres C1 and C2 is calculated as

C1C2 = sqrt((x1 – x2)2 + (y1 – y2)2).

There are three conditions that arise.

1. If C1C2 <= R1 – R2: Circle B is inside A.
2. If C1C2 <= R2 – R1: Circle A is inside B.
3. If C1C2 < R1 + R2: Circle intersects each other.
4. If C1C2 == R1 + R2: Circle A and B are in touch with each other.
5. Otherwise, Circle A and B do not overlap

Below is the implementation of the above approach:

## C++

 `// C++ program to check if two` `// circles touch each other or not.` `#include ` `using` `namespace` `std;`   `int` `circle(``int` `x1, ``int` `y1, ``int` `x2, ``int` `y2, ``int` `r1, ``int` `r2)` `{` `    ``double` `d = ``sqrt``((x1 - x2) * (x1 - x2)` `                         ``+ (y1 - y2) * (y1 - y2));`   `    ``if` `(d <= r1 - r2) {` `        ``cout << ``"Circle B is inside A"``;` `    ``}` `    ``else` `if` `(d <= r2 - r1) {` `        ``cout << ``"Circle A is inside B"``;` `    ``}` `    ``else` `if` `(d < r1 + r2) {` `        ``cout << ``"Circle intersect to each other"``;` `    ``}` `    ``else` `if` `(d == r1 + r2) {` `        ``cout << ``"Circle touch to each other"``;` `    ``}` `    ``else` `{` `        ``cout << ``"Circle not touch to each other"``;` `    ``}` `}`   `// Driver code` `int` `main()` `{` `    ``int` `x1 = -10, y1 = 8;` `    ``int` `x2 = 14, y2 = -24;` `    ``int` `r1 = 30, r2 = 10;` `    ``circle(x1, y1, x2, y2, r1, r2);`   `    ``return` `0;` `}`

## Java

 `// Java program to check if two` `// circles touch each other or not.` `import` `java.io.*;`   `class` `GFG {` `    ``static` `void` `circle(``int` `x1, ``int` `y1, ``int` `x2, ``int` `y2,` `                       ``int` `r1, ``int` `r2)` `    ``{` `        ``double` `d = Math.sqrt((x1 - x2) * (x1 - x2)` `                             ``+ (y1 - y2) * (y1 - y2));`   `        ``if` `(d <= r1 - r2) {` `            ``System.out.println(``"Circle B is inside A"``);` `        ``}` `        ``else` `if` `(d <= r2 - r1) {` `            ``System.out.println(``"Circle A is inside B"``);` `        ``}` `        ``else` `if` `(d < r1 + r2) {` `            ``System.out.println(``"Circle intersect"` `                               ``+ ``" to each other"``);` `        ``}` `        ``else` `if` `(d == r1 + r2) {` `            ``System.out.println(``"Circle touch to"` `                               ``+ ``" each other"``);` `        ``}` `        ``else` `{` `            ``System.out.println(``"Circle not touch"` `                               ``+ ``" to each other"``);` `        ``}` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `x1 = -``10``, y1 = ``8``;` `        ``int` `x2 = ``14``, y2 = -``24``;` `        ``int` `r1 = ``30``, r2 = ``10``;` `        ``circle(x1, y1, x2, y2, r1, r2);` `    ``}` `}`   `// This article is contributed by vt_m.`

## Python3

 `# Python program to check if two` `# circles touch each other or not.`   `import` `math`   `# Function to check if two circles touch each other` `def` `circle(x1, y1, x2, y2, r1, r2):` `    ``d ``=` `math.sqrt((x1 ``-` `x2) ``*` `(x1 ``-` `x2) ``+` `(y1 ``-` `y2) ``*` `(y1 ``-` `y2))`   `    ``if``(d <``=` `r1 ``-` `r2):` `        ``print``(``"Circle B is inside A"``)` `    ``elif``(d <``=` `r2 ``-` `r1):` `        ``print``(``"Circle A is inside B"``)` `    ``elif``(d < r1 ``+` `r2):` `        ``print``(``"Circle intersect to each other"``)` `    ``elif``(d ``=``=` `r1 ``+` `r2):` `        ``print``(``"Circle touch to each other"``)` `    ``else``:` `        ``print``(``"Circle not touch to each other"``)`   `# Driver code`   `x1, y1 ``=` `-``10``, ``8` `x2, y2 ``=` `14``, ``-``24` `r1, r2 ``=` `30``, ``10`   `# Function call` `circle(x1, y1, x2, y2, r1, r2)`   `# This code is contributed by Aman Kumar`

## C#

 `// C# program to check if two` `// circles touch each other or not.` `using` `System;`   `class` `GFG {` `    ``static` `void` `circle(``int` `x1, ``int` `y1, ``int` `x2, ``int` `y2,` `                    ``int` `r1, ``int` `r2)` `    ``{` `        ``double` `d = Math.Sqrt((x1 - x2) * (x1 - x2)` `                            ``+ (y1 - y2) * (y1 - y2));`   `        ``if` `(d <= r1 - r2) {` `            ``Console.Write(``"Circle B is inside A"``);` `        ``}` `        ``else` `if` `(d <= r2 - r1) {` `            ``Console.Write(``"Circle A is inside B"``);` `        ``}` `        ``else` `if` `(d < r1 + r2) {` `            ``Console.Write(``"Circle intersect"` `                            ``+ ``" to each other"``);` `        ``}` `        ``else` `if` `(d == r1 + r2) {` `            ``Console.Write(``"Circle touch to"` `                            ``+ ``" each other"``);` `        ``}` `        ``else` `{` `            ``Console.Write(``"Circle not touch"` `                            ``+ ``" to each other"``);` `        ``}` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main(String[] args)` `    ``{` `        ``int` `x1 = -10, y1 = 8;` `        ``int` `x2 = 14, y2 = -24;` `        ``int` `r1 = 30, r2 = 10;` `        ``circle(x1, y1, x2, y2, r1, r2);` `    ``}` `}`   `// This article is contributed by Pushpesh Raj.`

## Javascript

 `// JavaScript program to check if two circles touch each other or not.`   `function` `circle(x1, y1, x2, y2, r1, r2) {` `    ``var` `d = Math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));`   `    ``if` `(d <= r1 - r2) {` `        ``console.log(``"Circle B is inside A"``);` `    ``} ``else` `if` `(d <= r2 - r1) {` `        ``console.log(``"Circle A is inside B"``);` `    ``} ``else` `if` `(d < r1 + r2) {` `        ``console.log(``"Circle intersect to each other"``);` `    ``} ``else` `if` `(d === r1 + r2) {` `        ``console.log(``"Circle touch to each other"``);` `    ``} ``else` `{` `        ``console.log(``"Circle not touch to each other"``);` `    ``}` `}`   `// Driver code` `var` `x1 = -10, y1 = 8;` `var` `x2 = 14, y2 = -24;` `var` `r1 = 30, r2 = 10;` `circle(x1, y1, x2, y2, r1, r2);` `// this code is contributed by devendra`

Output

`Circle touch to each other`

Time Complexity: O(log(n)) because using inbuilt sqrt function
Auxiliary Space: O(1)

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