# 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<time.h>`
2. `#include<stdlib.h>`
3. `#include<iostream>`
4. `#include<math.h>`
5. ` `
6. `using namespace std;`
7. `const int LOW = 0;`
8. `const int HIGH = 10;`
9. `int main(int argc, char **argv)`
10. `{`
11. `    time_t seconds;`
12. `    time(&seconds);`
13. `    srand((unsigned int) seconds);`
14. ` `
15. `    double x1, x2, y1, y2, x3, y3;`
16. `    double m1, m2, c1, c2, r;`
17. `    x1 = rand() % (HIGH - LOW + 1) + LOW;`
18. `    x2 = rand() % (HIGH - LOW + 1) + LOW;`
19. `    x3 = rand() % (HIGH - LOW + 1) + LOW;`
20. `    y1 = rand() % (HIGH - LOW + 1) + LOW;`
21. `    y2 = rand() % (HIGH - LOW + 1) + LOW;`
22. `    y3 = rand() % (HIGH - LOW + 1) + LOW;`
23. `    m1 = (y1 - y2) / (x1 - x2);`
24. `    m2 = (y3 - y2) / (x3 - x2);`
25. ` `
26. `    c1 = ((m1 * m2 * (y3 - y1)) + (m1 * (x2 + x3)) - (m2 * (x1 + x2))) / (2`
27. `            * (m1 - m2));`
28. `    c2 = ((((x1 + x2) / 2) - c1) / (-1 * m1)) + ((y1 + y2) / 2);`
29. `    r = sqrt(((x3 - c1) * (x3 - c1)) + ((y3 - c2) * (y3 - c2)));`
30. `    cout << "The points on the circle are: (" << x1 << ", " << y1 << "), ("`
31. `            << x2 << ", " << y2 << "), (" << x3 << ", " << y3 << ")";`
32. `    cout << "\nThe center of the circle is (" << c1 << ", " << c2`
33. `            << ") and radius is " << r;`
34. ` `
35. `    cout << "\nEnter the point : <x>,<y>";`
36. `    int x, y;`
37. `    cin >> x;`
38. `    cin >> y;`
39. ` `
40. `    double s = ((x - c1) * (x - c1)) + ((y - c2) * (y - c1)) - (r * r);`
41. `    if (s < 0)`
42. `        cout << "\nThe point lies inside the circle";`
43. `    else if (s > 0)`
44. `        cout << "\nThe point lies outside the circle";`
45. `    else`
46. `        cout << "\nThe point lies on the circle";`
47. `    return 0;`
48. `}`

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)

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