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# 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  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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