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 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;
} |
Java
// 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 |
Python3
# 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 |
C#
// 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 |
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 chord function diameter(r)
{ document.write( "The length of the longest chord"
+ " or diameter of the circle is "
+ 2 * r);
} // Driver code // Get the radius var r = 4;
// Find the diameter diameter(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)