Length of the chord the circle if length of the another chord which is equally inclined through the diameter is given

Given are two chords which are equally inclined through the diameter of the circle. Length of one chord is given. The task is to find the length of another chord.

Examples:

Input: z = 48
Output: 48 degrees

Input: z = 93
Output: 93 degrees

Approach:

  • Let AB and AC be the two chords of the circle having the center at O.
  • now, in the figure we see,
    OL is perpendicular to AB and OM is perpendicular to AC
  • in triangle OLA and triangle OMA,
    angle OLA = angle OMA = 90 degrees
    angle OAL = angle OAM(as the chords are inclined equally through the diameter)
    OA = OA(common side)
  • so triangle OLA and triangle OMA are congruent to each other.
  • So, OL = OM
  • and we know, equal chords are equidistant from the center, so Length of AB and AC will be same.

If two chords are equally inclined through the diameter of the same circle, then they are of equal length.

Below is the implementation of the above approach:

C++

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// C++ program to find
// the length of the chord the circle
// if length of the another chord
// which is equally inclined
// through the diameter is given
  
#include <bits/stdc++.h>
using namespace std;
  
void lengchord(int z)
{
    cout << "The length is "
         << z << endl;
}
  
// Driver code
int main()
{
    int z = 48;
    lengchord(z);
    return 0;
}

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Java

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// Java program to find
// the length of the chord the circle
// if length of the another chord
// which is equally inclined
// through the diameter is given
import java.io.*;
  
class GFG 
{
      
static void lengchord(int z)
{
    System.out.println ("The length is "+ z );
}
  
// Driver code
public static void main (String[] args) 
{
  
    int z = 48;
    lengchord(z);
}
}
  
// The code has been contributed by ajit. 

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Python3

# Python3 program to find
# the length of the chord of the circle
# if length of the other chord
# which is equally inclined
# through the diameter is given
def lengchord(z):
print(“The length is “, end = “”);
print(z);

# Driver code
z = 48;
lengchord(z);

# This code is contributed
# by Princi Singh

C#

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// C# program to find
// the length of the chord the circle
// if length of the another chord
// which is equally inclined
// through the diameter is given
using System;
  
class GFG
{
          
static void lengchord(int z)
{
    Console.WriteLine("The length is "+ z );
}
  
// Driver code
static public void Main ()
{
          
    int z = 48;
    lengchord(z);
}
}
  
// The code has been contributed by Tushil

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Output:

The length is 48


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Improved By : jit_t, princi singh



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