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 <string.h>
```
```
#include <stdio.h>
```
```
#include <stdlib.h>
```
```
 
```
```
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)));

```
 
```

    printf("The points on the circle are: (%lf, %lf), (%lf, %lf), (%lf, %lf)\n",

```
            x1, y1, x2, y2, x3, y3);
```

    printf("The center of the circle is: (%lf, %lf) and radius is: %lf", c1,

```
            c2, r);
```
```
 
```

    printf("\nEnter the point : <x>,<y>");

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    int x, y;
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```
    scanf("%lf", &x);
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```
    scanf("%lf", &y);
```
```
 
```

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

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

        printf("\nThe point lies inside the circle");

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

        printf("\nThe point lies outside the circle");

```
    else
```

        printf("\nThe point lies on the circle");

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

Output:

$ gcc PointWRTCircle.c
$ ./a.out
 
The points on the circle are: (10.000000, 0.000000), (8.000000, 4.000000), (7.000000, 2.000000)
The center of the circle is: (9.250000, 1.875000) and radius is: 2.253470
Enter the point : <x>,<y> 
2 3
The point lies outside the circle

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