Find the Diameter or Longest chord of a Circle

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++

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// 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 chord
void diameter(double r)
{
    cout << "The length of the longest chord"
         << " or diameter of the circle is "
         << 2 * r << endl;
}
  
// Driver code
int main()
{
  
    // Get the radius
    double r = 4;
  
    // Find the diameter
    diameter(r);
  
    return 0;
}

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Java

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// Java program to find
// the longest chord or diameter
// of the circle whose radius is given
class GFG 
{
      
// Function to find the longest chord
static void diameter(double r)
{
    System.out.println("The length of the longest chord"
        + " or diameter of the circle is "
        + 2 * r);
}
  
// Driver code
public static void main(String[] args)
{
      
    // Get the radius
    double r = 4;
  
    // Find the diameter
    diameter(r);
}
}
  
// This code contributed by Rajput-Ji

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Python3

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# Python3 program to find
# the longest chord or diameter
# of the circle whose radius is given
  
# Function to find the longest chord
def diameter(r):
  
    print("The length of the longest chord"
        ," or diameter of the circle is "
        ,2 * r)
  
  
# Driver code
  
# Get the radius
r = 4
  
# Find the diameter
diameter(r)
  
# This code is contributed by mohit kumar

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C#

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// C# program to find
// the longest chord or diameter
// of the circle whose radius is given
using System;
  
class GFG 
{
      
// Function to find the longest chord
static void diameter(double r)
{
    Console.WriteLine("The length of the longest chord"
        + " or diameter of the circle is "
        + 2 * r);
}
  
// Driver code
public static void Main(String[] args)
{
      
    // Get the radius
    double r = 4;
  
    // Find the diameter
    diameter(r);
}
}
  
// This code has been contributed by 29AjayKumar

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PHP

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<?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
  
?>

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Output:

The length of the longest chord or diameter of the circle is 8


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