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

Below is the implementation of the above approach: 

C++

// 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;
}

Java

// 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..

Python3

# 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

C#

// 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..

Javascript

<script>
// javascript program to find the angle
// between a chord and a tangent
// when angle in the alternate segment is given

function anglechordtang(z)
{
document.write( "The angle between tangent"
               + " and the chord is "
               + z + " degrees");
}

// Driver code

var z = 48;
anglechordtang(z);

// This code is contributed by Amit Katiyar

</script>

Output:

The angle between tangent and the chord is 48 degrees

Time Complexity: O(1)

Auxiliary Space: O(1)