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:
- 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 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 givenclass 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 givenimport 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
<?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)
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
