# 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*π/180)**(here x deg is converted in radians) - So,
**d = rsin(x*π/180)**

therefore,**2d = 2rsin(x*π/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; ` `} ` |

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## 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 ` |

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## 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 ` |

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## 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 ` |

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## 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 ` ` ` `?> ` |

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**Output:**

The length of the chord of the circle is 7.12603

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