C++ Program to Find if a Point Lies Inside or Outside a Circle

This is a C++ Program to Check if a Point d lies Inside or Outside a Circle Defined by Points a, b, c in a Plane. For any point t (xt, yt) on the plane, its position with respect to the circle defined by 3 points (x1, y1) , (x2, y2), (x3, y3).
s = (x-xt)^2 + (y-yt)^2 – r*r
If s < 0, t lies inside the circle; if s > 0, t lies outside the circle; if s = 0, t lies on the circle.

Here is source code of the C++ Program to Check if a Point d lies Inside or Outside a Circle Defined by Points a, b, c in a Plane. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

```
#include<time.h>
```
```
#include<stdlib.h>
```
```
#include<iostream>
```
```
#include<math.h>
```
```
 
```
```
using namespace std;
```
```
const int LOW = 0;
```
```
const int HIGH = 10;
```
```
int main(int argc, char **argv)
```
```
{
```
```
    time_t seconds;
```
```
    time(&seconds);
```
```
    srand((unsigned int) seconds);
```
```
 
```
```
    double x1, x2, y1, y2, x3, y3;
```
```
    double m1, m2, c1, c2, r;
```

    x1 = rand() % (HIGH - LOW + 1) + LOW;

    x2 = rand() % (HIGH - LOW + 1) + LOW;

    x3 = rand() % (HIGH - LOW + 1) + LOW;

    y1 = rand() % (HIGH - LOW + 1) + LOW;

    y2 = rand() % (HIGH - LOW + 1) + LOW;

    y3 = rand() % (HIGH - LOW + 1) + LOW;

```
    m1 = (y1 - y2) / (x1 - x2);
```
```
    m2 = (y3 - y2) / (x3 - x2);
```
```
 
```

    c1 = ((m1 * m2 * (y3 - y1)) + (m1 * (x2 + x3)) - (m2 * (x1 + x2))) / (2

```
            * (m1 - m2));
```

    c2 = ((((x1 + x2) / 2) - c1) / (-1 * m1)) + ((y1 + y2) / 2);

    r = sqrt(((x3 - c1) * (x3 - c1)) + ((y3 - c2) * (y3 - c2)));

    cout << "The points on the circle are: (" << x1 << ", " << y1 << "), ("

            << x2 << ", " << y2 << "), (" << x3 << ", " << y3 << ")";

    cout << "\nThe center of the circle is (" << c1 << ", " << c2

```
            << ") and radius is " << r;
```
```
 
```

    cout << "\nEnter the point : <x>,<y>";

```
    int x, y;
```
```
    cin >> x;
```
```
    cin >> y;
```
```
 
```

    double s = ((x - c1) * (x - c1)) + ((y - c2) * (y - c1)) - (r * r);

```
    if (s < 0)
```

        cout << "\nThe point lies inside the circle";

```
    else if (s > 0)
```

        cout << "\nThe point lies outside the circle";

```
    else
```

        cout << "\nThe point lies on the circle";

```
    return 0;
```
```
}
```

Output:

$ g++ PointWRTCircle.cpp
$ a.out
 
The points on the circle are: (2, 5), (10, 8), (3, 6)
The center of the circle is (8.7, 13.7) and radius is 9.58019
Enter the point : <x>,<y> 1 2
 
The point lies outside the circle
 
The points on the circle are: (0, 6), (9, 7), (6, 10)
The center of the circle is (4.6, 7.4) and radius is 2.95296
Enter the point : <x>,<y>6 5
 
The point lies inside the circle
------------------
(program exited with code: 0)
Press return to continue

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