# Length of the chord of the circle whose radius and the angle subtended at the center by the chord is given

Given a circle whose radius and the angle subtended at the centre by its chord is given. The task is to find the length of the chord.**Examples:**

Input:r = 4, x = 63Output:4.17809Input::r = 9, x = 71Output::10.448

**Approach**:

- Let the circle has center at
**O**and has radius**r**, and it’s chord be**AB**. - length of the chord be
**2d**, and the angle subtended by it on the center be**2x**degrees. - As the perpendicular dropped at the chord bisects the chord so, the perpendicular also equally divides the subtended angle
**2x**in**x**degrees. - So, from the diagram,
**d/r = sin(x*Ï€/180)**(here x deg is converted in radians) - So,
**d = rsin(x*Ï€/180)**

therefore,**2d = 2rsin(x*Ï€/180)**

- So,

Below is the implementation of the above approach:

## C++

`// C++ program to find the length chord` `// of the circle whose radius` `// and the angle subtended at the centre` `// is also given` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the length of the chord` `void` `length_of_chord(` `double` `r, ` `double` `x)` `{` ` ` `cout << ` `"The length of the chord"` ` ` `<< ` `" of the circle is "` ` ` `<< 2 * r * ` `sin` `(x * (3.14 / 180))` ` ` `<< endl;` `}` `// Driver code` `int` `main()` `{` ` ` `double` `r = 4, x = 63;` ` ` `length_of_chord(r, x);` ` ` `return` `0;` `}` |

## Java

`// Java program to find the length chord` `// of the circle whose radius` `// and the angle subtended at the centre` `// is also given` `class` `GFG` `{` `// Function to find the length of the chord` `static` `void` `length_of_chord(` `double` `r, ` `double` `x)` `{` ` ` `System.out.println(` `"The length of the chord"` ` ` `+ ` `" of the circle is "` ` ` `+ ` `2` `* r * Math.sin(x * (` `3.14` `/ ` `180` `)));` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `double` `r = ` `4` `, x = ` `63` `;` ` ` `length_of_chord(r, x);` `}` `}` `// This code contributed by Rajput-Ji` |

## Python3

`# Python3 program to find the length chord` `# of the circle whose radius` `# and the angle subtended at the centre` `# is also given` `import` `math as mt` `# Function to find the length of the chord` `def` `length_of_chord(r, x):` ` ` `print` `(` `"The length of the chord"` ` ` `,` `" of the circle is "` ` ` `,` `2` `*` `r ` `*` `mt.sin(x ` `*` `(` `3.14` `/` `180` `)))` `# Driver code` `r ` `=` `4` `x ` `=` `63` `;` `length_of_chord(r, x)` `# This code is contributed by mohit kumar` |

## C#

`// C# program to find the length chord` `// of the circle whose radius` `// and the angle subtended at the centre` `// is also given` `using` `System;` `class` `GFG` `{` ` ` ` ` `// Function to find the length of the chord` ` ` `static` `void` `length_of_chord(` `double` `r, ` `double` `x)` ` ` `{` ` ` `Console.WriteLine(` `"The length of the chord"` `+` ` ` `" of the circle is "` `+` ` ` `2 * r * Math.Sin(x * (3.14 / 180)));` ` ` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main(String[] args)` ` ` `{` ` ` `double` `r = 4, x = 63;` ` ` `length_of_chord(r, x);` ` ` `}` `}` `// This code is Contributed by Naman_Garg` |

## PHP

`<?php` `// PHP program to find the length chord` `// of the circle whose radius and the` `// angle subtended at the centre` `// is also given` `// Function to find the length of the chord` `function` `length_of_chord(` `$r` `, ` `$x` `)` `{` ` ` `echo` `"The length of the chord"` `,` ` ` `" of the circle is "` ` ` `,2 * ` `$r` `* sin(` `$x` `* (3.14 / 180)) ;` ` ` `}` ` ` `// Driver code` ` ` `$r` `= 4; ` `$x` `= 63;` ` ` `length_of_chord(` `$r` `, ` `$x` `);` ` ` `// This code is contributed by Ryuga` `?>` |

## Javascript

`<script>` `// JavaScript program to find the length chord` `// of the circle whose radius` `// and the angle subtended at the centre` `// is also given` `// Function to find the length of the chord` `function` `length_of_chord(r, x)` `{` ` ` `document.write(` `"The length of the chord"` ` ` `+ ` `" of the circle is "` ` ` `+ 2 * r * Math.sin(x * (3.14 / 180))` ` ` `+ ` `"<br>"` `);` `}` `// Driver code` ` ` `let r = 4, x = 63;` ` ` `length_of_chord(r, x);` `// This code is contributed by Surbhi Tyagi.` `</script>` |

**Output:**

The length of the chord of the circle is 7.12603

Time Complexity: O(1)

Auxiliary Space: O(1)