# Angle subtended by an arc at the centre of a circle

Given the angle subtended by an arc at the circle circumference X, the task is to find the angle subtended by an arc at the centre of a circle.

For eg in the below given image, you are given angle X and you have to find angle Y.

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**Examples:**

Input:X = 30Output:60Input:X = 90Output:180

**Approach:**

- When we draw the radius AD and the chord CB, we get three small triangles.
- The three triangles ABC, ADB and ACD are isosceles as AB, AC and AD are radiuses of the circle.
- So in each of these triangles, the two acute angles (s, t and u) in each are equal.
- From the diagram, we can see

D = t + u (i)

- In triangle ABC,

s + s + A = 180 (angles in triangle) ie, A = 180 - 2s (ii)

- In triangle BCD,

(t + s) + (s + u) + (u + t) = 180 (angles in triangle again) so 2s + 2t + 2u = 180 ie 2t + 2u = 180 - 2s (iii)

A = 2t + 2u = 2D from (i), (ii) and (iii)

- Hence Proved that ‘
**the angle at the centre is twice the angle at the circumference**‘.

Below is the implementation of the above approach:

## C++

`// C++ implementation of the approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find Angle` `// subtended by an arc` `// at the centre of a circle` `int` `angle(` `int` `n)` `{` ` ` `return` `2 * n;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `n = 30;` ` ` `cout << angle(n);` ` ` `return` `0;` `}` |

## Java

`// Java implementation of the approach` `import` `java.io.*;` `class` `GFG` `{` ` ` `// Function to find Angle subtended` `// by an arc at the centre of a circle` `static` `int` `angle(` `int` `n)` `{` ` ` `return` `2` `* n;` `}` `// Driver code` `public` `static` `void` `main (String[] args)` `{` ` ` `int` `n = ` `30` `;` ` ` `System.out.println(angle(n));` `}` `}` `// This code is contributed by ajit.` |

## Python3

`# Python3 implementation of the approach` `# Function to find Angle` `# subtended by an arc` `# at the centre of a circle` `def` `angle(n):` ` ` `return` `2` `*` `n` `# Driver code` `n ` `=` `30` `print` `(angle(n))` `# This code is contributed by Mohit Kumar` |

## C#

`// C# implementation of the approach` `using` `System;` `class` `GFG` `{` ` ` `// Function to find Angle subtended` `// by an arc at the centre of a circle` `static` `int` `angle(` `int` `n)` `{` ` ` `return` `2 * n;` `}` `// Driver code` `public` `static` `void` `Main()` `{` ` ` `int` `n = 30;` ` ` `Console.Write(angle(n));` `}` `}` `// This code is contributed by Akanksha_Rai` |

## Javascript

`<script>` `// JavaScript implementation of the approach` `// Function to find Angle` `// subtended by an arc` `// at the centre of a circle` `function` `angle(n)` `{` ` ` `return` `2 * n;` `}` `// Driver code` ` ` `let n = 30;` ` ` `document.write(angle(n));` `// This code is contributed by Surbhi Tyagi.` `</script>` |

**Output:**

60

**Time Complexity:** O(1)