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

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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.

1. `#include <string.h>`
2. `#include <stdio.h>`
3. `#include <stdlib.h>`
4. ` `
5. `const int LOW = 0;`
6. `const int HIGH = 10;`
7. `int main(int argc, char **argv) {`
8. `    time_t seconds;`
9. `    time(&seconds);`
10. `    srand((unsigned int) seconds);`
11. ` `
12. `    double x1, x2, y1, y2, x3, y3;`
13. `    double m1, m2, c1, c2, r;`
14. `    x1 = rand() % (HIGH - LOW + 1) + LOW;`
15. `    x2 = rand() % (HIGH - LOW + 1) + LOW;`
16. `    x3 = rand() % (HIGH - LOW + 1) + LOW;`
17. `    y1 = rand() % (HIGH - LOW + 1) + LOW;`
18. `    y2 = rand() % (HIGH - LOW + 1) + LOW;`
19. `    y3 = rand() % (HIGH - LOW + 1) + LOW;`
20. `    m1 = (y1 - y2) / (x1 - x2);`
21. `    m2 = (y3 - y2) / (x3 - x2);`
22. ` `
23. `    c1 = ((m1 * m2 * (y3 - y1)) + (m1 * (x2 + x3)) - (m2 * (x1 + x2))) / (2`
24. `            * (m1 - m2));`
25. `    c2 = ((((x1 + x2) / 2) - c1) / (-1 * m1)) + ((y1 + y2) / 2);`
26. `    r = sqrt(((x3 - c1) * (x3 - c1)) + ((y3 - c2) * (y3 - c2)));`
27. ` `
28. `    printf("The points on the circle are: (%lf, %lf), (%lf, %lf), (%lf, %lf)\n",`
29. `            x1, y1, x2, y2, x3, y3);`
30. `    printf("The center of the circle is: (%lf, %lf) and radius is: %lf", c1,`
31. `            c2, r);`
32. ` `
33. `    printf("\nEnter the point : <x>,<y>");`
34. `    int x, y;`
35. `    scanf("%lf", &x);`
36. `    scanf("%lf", &y);`
37. ` `
38. `    double s = ((x - c1) * (x - c1)) + ((y - c2) * (y - c1)) - (r * r);`
39. `    if (s < 0)`
40. `        printf("\nThe point lies inside the circle");`
41. `    else if (s > 0)`
42. `        printf("\nThe point lies outside the circle");`
43. `    else`
44. `        printf("\nThe point lies on the circle");`
45. `    return 0;`
46. `}`

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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