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

In case of a given circle, chord and tangent is met at a particular point. The angle in the alternate segment is provided. The main job here is to find the angle between the chord and the tangent.

Examples

Input: z = 40
Output: 40 degrees
Input: z = 60
Output: 60 degrees

Approach

• Let, angle QPR is the given angle in the alternate segment.

• Let, the angle between the chord and circle = angle RQY = a

• Because line drawn from center on the tangent is perpendicular,

• So, angle CQR = 90-a

• As, CQ = CR = radius of the circle

• So, angle CRQ = 90-a

• Now, in triangle CQR,

  • angle CQR + angle CRQ + angle QCR = 180

  • angle QCR = 180 - (90-a) - (90-a)

  • angle QCR = 2a

• As angle at the circumference of a circle be the half the angle at the centre subtended by the same arc,so, angle QPR = a

• Hence, angle QPR = angle RQY

The approach is implemented in following way −

Example

// C++ program to find the angle
// between a chord and a tangent
// at the time when angle in the alternate segment is given
#include <bits/stdc++.h>
using namespace std;
void anglechordtang(int z1){
   cout<< "The angle between tangent"
   <<" and the chord is "
   << z1 <<" degrees" << endl;
}
// Driver code
int main(){
   int z1 = 40;
   anglechordtang(z1);
   return 0;
}

Output

The angle between tangent and the chord is 40 degrees