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 chord void 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 code int 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 chord static 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 code public 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 chord def length_of_chord(r, x):
print ( "The length of the chord"
, " of the circle is "
, 2 * r * mt.sin(x * ( 3.14 / 180 )))
# Driver code r = 4
x = 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)