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

• Last Updated : 31 May, 2021

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. Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

Examples:

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

 ``
Output:
`60`

Time Complexity: O(1)

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