Angle between a chord and a tangent when angle in the alternate segment is given

Given a circle whose chord and tangent meet at a particular point. The angle in the alternate segment is given. The task here is to find the angle between the chord and the tangent.

Examples:

Input: z = 48
Output: 48 degrees

Input: z = 64
Output: 64 degrees



Approach:

  • Let, angle BAC is the given angle in the alternate segment.
  • let, the angle between the chord and circle = angle CBY = z
  • as line drawn from center on the tangent is perpendicular,
  • so, angle OBC = 90-z
  • as, OB = OC = radius of the circle
  • so, angle OCB = 90-z
  • now, in triangle OBC,
    angle OBC + angle OCB + angle BOC = 180
    angle BOC = 180 – (90-z) – (90-z)
    angle BOC = 2z
  • as angle at the circumference of a circle is half the angle at the centre subtended by the same arc,
    so, angle BAC = z
  • hence, angle BAC = angle CBY

The angle between a chord and a tangent is equal to the angle in the alternate segment.

Below is the implementation of the above approach:

C++

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// C++ program to find the angle
// between a chord and a tangent
// when angle in the alternate segment is given
  
#include <bits/stdc++.h>
using namespace std;
  
void anglechordtang(int z)
{
    cout << "The angle between tangent"
         << " and the chord is "
         << z << " degrees" << endl;
}
  
// Driver code
int main()
{
    int z = 48;
    anglechordtang(z);
    return 0;
}

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Java

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// Java program to find the angle
// between a chord and a tangent
// when angle in the alternate segment is given
import java.io.*;
  
class GFG 
{
  
    static void anglechordtang(int z)
    {
        System.out.print( "The angle between tangent"
            + " and the chord is "
            + z + " degrees");
    }
      
    // Driver code
    public static void main (String[] args) 
    {
        int z = 48;
        anglechordtang(z);
    }
}
  
// This code is contributed by anuj_67..

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Python3

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# Python3 program to find the angle
# between a chord and a tangent
# when angle in the alternate segment is given
def anglechordtang(z):
  
    print("The angle between tangent"
          "and the chord is", z , "degrees");
  
# Driver code
z = 48;
anglechordtang(z);
  
# This code is contributed
# by Princi Singh

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C#

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// C# program to find the angle
// between a chord and a tangent
// when angle in the alternate segment is given
using System;
  
class GFG 
{
  
    static void anglechordtang(int z)
    {
        Console.WriteLine( "The angle between tangent"
            + " and the chord is "
            + z + " degrees");
    }
      
    // Driver code
    public static void Main () 
    {
        int z = 48;
        anglechordtang(z);
    }
}
  
// This code is contributed by anuj_67..

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Output:

The angle between tangent and the chord is 48 degrees


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Improved By : vt_m, princi singh



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