# Check whether a point exists in circle sector or not.

We have a circle centered at origin (0, 0). As input we are given with starting angle of the circle sector and the size of the circle sector in percentage.
Examples:

```Input :  Radius = 8
StartAngle = 0
Percentage = 12
x = 3 y = 4
Output : Point (3, 4) exists in the circle
sector

Startangle = 45
Percentage = 25
x = 3 y = 4
Output : Point (3, 4) does not exist in
the circle sector
```

Source:wikibooks.org

In this image starting angle is 0 degree, radius r and suppose that percentage of colored area is 12% then we calculate Ending Angle as 360/percentage + starting angle.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

To find whether a point (x, y) exists in a circle sector (centered at origin) or not we find polar coordinates of that point and then go through the following steps:

1. Convert x, y to polar coordinates using this
Angle = atan(y/x); Radius = sqrt(x * x + y * y);
```// C++ program to check if a point lies inside a circle
// sector.
#include<bits/stdc++.h>
using namespace std;

void checkPoint(int radius, int x, int y, float percent,
float startAngle)
{
// calculate endAngle
float endAngle = 360/percent + startAngle;

// Calculate polar co-ordinates
float Angle = atan(y/x);

// or not and Angle is between startAngle and endAngle
// or not
printf("Point (%d, %d) exist in the circle sector\n", x, y);
else
printf("Point (%d, %d) does not exist in the circle sector\n",
x, y);
}

// Driver code
int main()
{
int radius = 8, x = 3, y = 4;
float percent  = 12, startAngle = 0;
return 0;
}
```

Output: Point(3, 4) exists in the circle sector

```Time complexity = O(1)
```

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