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

Last Updated : 07 Jun, 2022

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 = 63
Output: 4.17809

Input:: r = 9, x = 71
Output:: 10.448

Approach

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

6. 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 using namespace std; // Function to find the length of the chordvoid 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 codeint 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 chordstatic 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 codepublic 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 chorddef length_of_chord(r, x):     print("The length of the chord"        ," of the circle is "        ,2 * r * mt.sin(x * (3.14 / 180)))  # Driver coder = 4x = 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



## Javascript



Output:
The length of the chord of the circle is 7.12603

Time Complexity: O(1)

Auxiliary Space: O(1)