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

10 Mar, 2021
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++
Java
Python3
C#
Javascript
// 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 codeint main(){    int z = 48;    anglechordtang(z);    return 0;}
// Java program to find the angle// between a chord and a tangent// when angle in the alternate segment is givenimport 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 program to find the angle# between a chord and a tangent# when angle in the alternate segment is givendef anglechordtang(z):     print("The angle between tangent",          "and the chord is", z , "degrees"); # Driver codez = 48;anglechordtang(z); # This code is contributed# by Princi Singh
// C# program to find the angle// between a chord and a tangent// when angle in the alternate segment is givenusing 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..
<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>
The angle between tangent and the chord is 48 degrees
 
vt_m
princi singh
amit143katiyar
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Mathematical
Geometric
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