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# 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

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