# Length of rope tied around three equal circles touching each other

Given **r** is the radius of three equal circles touching each other. The task is to find the length of the rope tied around the circles as shown below:

**Examples:**

Input:r = 7

Output:86

Input:r = 14

Output:172

**Approach:** As it can be clearly seen from above image, the part of the length of rope which is not touching the circle is **2r + 2r + 2r = 6r**.

The part of the rope which is touching the circles make a sector of 120 degrees on each circle. Thus, three sectors of 120 degrees each can be considered as a complete one circle of 360 degrees.

Therefore, Length of rope touching the circle is **2 * PI * r** where **PI = 22 / 7** and **r** is the radius of the circle.

Hence, the total length of the rope will be **( 2 * PI * r ) + 6r**.

Below is the implementation of the above approach:

## CPP

`// C++ program to find the length ` `// of rope ` `#include<bits/stdc++.h> ` `using` `namespace` `std; ` `#define PI 3.14159265 ` ` ` `// Function to find the length ` `// of rope ` `float` `length_rope( ` `float` `r ) ` `{ ` ` ` `return` `( ( 2 * PI * r ) + 6 * r ); ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `float` `r = 7; ` ` ` `cout<<` `ceil` `(length_rope( r ))<<endl; ` ` ` `return` `0; ` `} ` |

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## C

`// C program to find the length ` `// of rope ` `#include <stdio.h> ` `#define PI 3.14159265 ` ` ` `// Function to find the length ` `// of rope ` `float` `length_rope( ` `float` `r ) ` `{ ` ` ` `return` `( ( 2 * PI * r ) + 6 * r ); ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `float` `r = 7; ` ` ` `printf` `(` `"%f"` `, ` ` ` `length_rope( r )); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java code to find the length ` `// of rope ` `import` `java.lang.*; ` ` ` `class` `GFG { ` ` ` ` ` `static` `double` `PI = ` `3.14159265` `; ` ` ` ` ` `// Function to find the length ` ` ` `// of rope ` ` ` `public` `static` `double` `length_rope(` `double` `r) ` ` ` `{ ` ` ` `return` `((` `2` `* PI * r) + ` `6` `* r); ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `main(String[] args) ` ` ` `{ ` ` ` `double` `r = ` `7` `; ` ` ` `System.out.println(length_rope(r)); ` ` ` `} ` `} ` |

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## Python3

`# Python3 code to find the length ` `# of rope ` `PI ` `=` `3.14159265` ` ` `# Function to find the length ` `# of rope ` `def` `length_rope( r ): ` ` ` `return` `( ( ` `2` `*` `PI ` `*` `r ) ` `+` `6` `*` `r ) ` ` ` `# Driver code ` `r ` `=` `7` `print` `( length_rope( r )) ` |

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## C#

`// C# code to find the length ` `// of rope ` `using` `System; ` ` ` `class` `GFG { ` ` ` `static` `double` `PI = 3.14159265; ` ` ` ` ` `// Function to find the length ` ` ` `// of rope ` ` ` `public` `static` `double` `length_rope(` `double` `r) ` ` ` `{ ` ` ` `return` `((2 * PI * r) + 6 * r); ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `double` `r = 7.0; ` ` ` `Console.Write(length_rope(r)); ` ` ` `} ` `} ` |

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## PHP

`<?php ` `// PHP program to find the ` `// length of rope ` `$PI` `= 3.14159265; ` ` ` `// Function to find the length ` `// of rope ` `function` `length_rope( ` `$r` `) ` `{ ` ` ` `global` `$PI` `; ` ` ` `return` `( ( 2 * ` `$PI` `* ` `$r` `) + 6 * ` `$r` `); ` `} ` ` ` `// Driver code ` `$r` `=7; ` `echo` `(length_rope( ` `$r` `)); ` `?> ` |

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**Output:**

86

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