Given a circle with radius ‘r’ is given, the task is to find the diameter or longest chord of the circle.
Examples:
Input: r = 4 Output: 8 Input: r = 9 Output: 18
Proof that the Longest chord of a circle is its Diameter:
- Draw circle O and any chord AB on it.
- From one endpoint of the chord, say A, draw a line segment through the centre. That is, draw a diameter.
- Now draw a radius from centre O to B.
- By the triangle inequality,
AB < AO + OB = r + r = 2r = d
- So, any chord that is not a diameter will be smaller than a diameter.
- So the largest chord is a diameter
Approach:
- The Longest chord of any circle is its diameter.
- Therefore, the diameter of a circle is twice the radius of it.
Length of the longest chord or diameter = 2r
Below is the implementation of the above approach:
C++
// C++ program to find// the longest chord or diameter// of the circle whose radius is given#include <bits/stdc++.h>using namespace std;// Function to find the longest chordvoid diameter(double r){ cout << "The length of the longest chord" << " or diameter of the circle is " << 2 * r << endl;}// Driver codeint main(){ // Get the radius double r = 4; // Find the diameter diameter(r); return 0;} |
Java
// Java program to find// the longest chord or diameter// of the circle whose radius is givenclass GFG { // Function to find the longest chordstatic void diameter(double r){ System.out.println("The length of the longest chord" + " or diameter of the circle is " + 2 * r);}// Driver codepublic static void main(String[] args){ // Get the radius double r = 4; // Find the diameter diameter(r);}}// This code contributed by Rajput-Ji |
Python3
# Python3 program to find# the longest chord or diameter# of the circle whose radius is given# Function to find the longest chorddef diameter(r): print("The length of the longest chord" ," or diameter of the circle is " ,2 * r)# Driver code# Get the radiusr = 4# Find the diameterdiameter(r)# This code is contributed by mohit kumar |
C#
// C# program to find// the longest chord or diameter// of the circle whose radius is givenusing System;class GFG { // Function to find the longest chordstatic void diameter(double r){ Console.WriteLine("The length of the longest chord" + " or diameter of the circle is " + 2 * r);}// Driver codepublic static void Main(String[] args){ // Get the radius double r = 4; // Find the diameter diameter(r);}}// This code has been contributed by 29AjayKumar |
PHP
<?php// PHP program to find // the longest chord or diameter // of the circle whose radius is given // Function to find the longest chord function diameter($r) { echo "The length of the longest chord" ," or diameter of the circle is " ,2 * $r << "\n"; } // Driver code // Get the radius $r = 4; // Find the diameter diameter($r); // This code is contributed by Ryuga?> |
Javascript
<script>// javascript program to find// the longest chord or diameter// of the circle whose radius is given // Function to find the longest chordfunction diameter(r){ document.write("The length of the longest chord" + " or diameter of the circle is " + 2 * r);}// Driver code // Get the radiusvar r = 4;// Find the diameterdiameter(r);// This code contributed by Princi Singh </script> |
Output:
The length of the longest chord or diameter of the circle is 8
Time Complexity: O(1)
Auxiliary Space: O(1)
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